Research ArticleResearch on the Identification of Key Nodes in the Process ofWeChat Epidemic Information Dissemination ASupernetwork Perspective

Peng Wu and Di Zhao

Institute of Management Science and Engineering Henan University Kaifeng 475004 China

Correspondence should be addressed to Peng Wu akasfd126com

Received 24 June 2020 Accepted 25 July 2020 Published 27 August 2020

Guest Editor Shaohui Wang

Copyright copy 2020 Peng Wu and Di Zhao is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

It is of great significance to comprehensively and reasonably identify the key nodes in the WeChat epidemic informationdissemination system First the recognition results can be used to guide the spread of epidemic-related information in WeChatsuch as accelerating the spread of valuable information or monitoring the spread of rumors Secondly the analysis of key nodeshelps us understand the evolution of the epidemic information dissemination network in WeChat and the analysis of key nodesalso helps us understand the modes andmethods of epidemic-related information dissemination inWeChat Finally the results ofthese studies may be generalized to other fields of social life is paper analyzes the composition of and relationship betweenepidemic-related information dissemination systems in WeChat and proposes a Supernetwork model for WeChat epidemicinformation dissemination on this basis In this study a comprehensive identification method of key nodes of the WeChatepidemic information dissemination system under the Supernetwork vision was constructed and the method is analyzed andverified through examples in this paper

1 Introduction

With the rapid development of information technology andthe increasingly complex social system the current infor-mation dissemination related to the epidemic situation isalso becomingmore andmore rapid If the spread of relevantpublic opinion or rumors in a network cannot be promptlyunderstood and effectively guided and managed the spreadof its outbreak will have catastrophic consequenceserefore it is necessary to conduct research and analysis onthe spread of information related to the epidemic situation[1]

Tencent released the ldquo2019 WeChat Annual Data Re-portrdquo in January 2020 e report stated that in 2019 thenumber of WeChat monthly active accounts exceeded 11billion [2] With such a huge monthly active user scaleWeChatrsquos role in the spread of epidemic information cannotbe underestimated

After the outbreak WeChat as a highly active and highlyconnected medium has become an important channel forthe public to understand and participate in the epidemicScholar Liu [3] used the framework analysis theory tosystematically analyze the top 200 WeChat posts using theQingbo Index over a period of time and found that the topposts on WeChat during the epidemic mainly showed thefollowing characteristics In terms of media report typesboth self-media and traditional media commonly guide thenetwork public opinion pattern In terms of the evolution ofpublic opinion online public opinion events frequentlyoccur and advance in waves In the news framework theresponse framework and the emotional framework have thehighest public acceptance and recognition rough theabove research Liu proposed that the guidance of publicopinion on the epidemic should strengthen the ldquostrengthrdquo ofrational dissemination pay attention to the ldquotemperaturerdquo ofhumanistic care and improve the ldquovalidityrdquo of public

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 6751686 10 pageshttpsdoiorg10115520206751686

opinion guidance Based on a full-sample empirical analysisof 2966 official WeChat public account articles from 42ldquodouble first-classrdquo universities Deng et al [4] found thatarticle topics information sources and emotional tenden-cies have a significant impact on communication effectsPublic opinion propaganda with a richer connotation ismore popular e original works of universitiesrsquo WeChatpublic accounts are more influential Public opinion pro-paganda with obvious ldquopositiverdquo or ldquonegativerdquo sentimentaltendencies has a significant impact on the communicationeffect but in different ways Readers who read short andconcise articles are more likely to keep reading until the endof the article and like the article Chen [5] found that rumorsshowed a rapid growth trend in the early stages of theoutbreak e formation and spread of rumors mainly oc-curs on WeChat and Weibo and the spread of rumors isdirectly related to the degree of government informationdisclosure Due to the strong relationship and semienclosedspace feature of WeChat WeChat rumors are mainly spreadthrough public accounts group chats private chats andcircles of friends ey have both interpersonal and grouptransmission characteristics and are extremely infectious Asthe number of confirmed diagnoses across the country beganto decline and some cities began to resume work thegovernment continued to disclose information about theepidemic in an open and transparent manner and relatedrumors began to decline During this period the govern-ment responded quickly to rumors and there graduallybecame fewer ldquounverifiedrdquo rumors At the same time thespread of strong relationships inWeChat groups allowed thepublic to receive a large amount of factual splicing fromrelatives and friends in different spaces which eliminatedrumors to a great extent e ambiguity in the communi-cation model improved the publicrsquos judgment and therumors lost their foundation for spreading Wan et al [6]used the case study method to establish the status quo of theldquofitness antiepidemic tweetsrdquo pushed by the 117 WeChatsubscription accounts they followed and found that theirmain features are the time and frequency of article postingwhich are consistent with the changes in the number ofconfirmed cases and the overall national prevention andcontrol deployment e online dissemination of content iscomprehensive and the amount of information is graduallydecreasing with the effective relief of the epidemic By an-alyzing popular words in WeChat Lu and Zhang [7] foundthat the development of the epidemic had a certain patternFirst of all people paid attention to which pathogen thedisease comes from the location of the outbreak and whatsymptoms appearen the public began to pay attention tothe source of pathogens the behavior and self-protection ofmedical staff and the needs of daily life On the other handpeople paid more attention to the epidemic situation inother places and the results of local control rough theanalysis of public concern we reviewed the developmenttrend of the epidemic which will set an example for futureepidemics It is believed that public health authorities willrely more on these social media to monitor the developmentof epidemics or pandemics in the future Judging from theexisting related results there are few studies in this field and

the use of Supernetwork theory to study the spread of ep-idemic information in WeChat is still rare

is article studies and analyzes the composition andrelationship between the epidemic-related informationdissemination systems in WeChat On this basis three typesof active and representative elements are establishednamely ordinary WeChat users WeChat groups andWeChat public accounts e three epidemic informationdissemination network relationships are combined andintegrated into a Supernetwork

2 Supernetwork Theory and WeChatSupernetwork Model Construction

Scholars previously used the term ldquoSupernetworkrdquo in thefields of computer systems genetics and transportationsystems to generally refer to complex systems with com-plicated nodes complicated relationships and networkswithin them In the American scholar Nagurneyrsquos work oninterwoven networks the network that is higher than andsurpasses the existing network is referred to as theldquoSupernetworkrdquo which helps to clearly define this term[8 9] Chinese scholars Academician Wang Zhongtuo andProfessor Wang Zhiping further proposed the relevantcharacteristics of the Supernetwork ey believe that theSupernetwork has one or more of the following charac-teristics (1) e network contains the network or it can besaid that the network is nested in the network (2) It has thecharacteristics of multiple layers and there are connectionswithin and between layers For example the protocol of theinformation network is multilayered and the transportationnetwork has a management layer a business layer and aphysical layer which are also multilayered (3) It has thecharacteristics of multiple levels and there is a connectionbetween these levels For example the information networkof an enterprise has multiple levels such as headquarterscompanies and departments (4) Its flow can have multi-dimensional characteristics For example aviation roadswater transportation and railways all have both freight andpassenger transportation (5) It has the characteristics ofmultiple attributes or multiple criteria For example thetransportation network needs to consider factors such ascost safety time and comfort at the same time and whentraveling in a city there are not only travel modes (such asself-driving public transportation or walking) but alsoroute options (6) It has the characteristics of congestion Forexample the transportation network has the problem ofcongestion as does the information network (7) Sometimesthere is a conflict between individual optimization andglobal optimization which requires coordination [9]

Recent research on Supernetworks can be divided intothree directions based on variational inequalities [10ndash12]the work mainly intends to transform the multilayeredmultistandard Supernetwork balance model into an opti-mization problem and then use evolutionary variation in-equality to solve the problem [9]e system science [13ndash16]research studies the Supernetwork as a whole as well asindividual aspects including the study of the relationshipbetween the network and the network in the Supernetwork

2 Mathematical Problems in Engineering

the study of the network using the relationship between theoutside and the network and the study of overall perfor-mance e modeling work of this article is mainly inspiredand helped by some research results in this area Researchbased on hypergraphs [17] is considered to be another moreimportant research direction It is mostly used to solve theproblem of different textures between edges and nodes innetwork research Hypergraphs are used to describe thesystem and study the statistical characteristics of the net-worke research on Supernetworks has developed rapidlyand its application fields are also relatively wide such asknowledge management supply chains transportation fi-nancial management advertising e-commerce biology andorganization and cooperation [18] However Supernetworktheory andmethods are rarely applied to the field ofWeChatepidemic information dissemination

WeChat public accounts common WeChat users andWeChat groups are the main outlets through which epi-demic information is spread in WeChat e public accountmainly disseminates information through the weak rela-tionship between the public account and the fanse publicaccount and the fans form a star network Relativelyspeaking the communication speed is fast and the spread iswide but the audience trusts the public account to releaseinformation though this is not the most trusted source ofinformation

e ordinary users of WeChat mainly spread informa-tion through the strong relationship between ordinary usersrsquofriends e information publisher and information receiverin the circle of friends also form a star network Because ofthe relationships between acquaintances the informationposted in the circle of friends is related to the circle offriends Members tend to believe this information more butthe information in the circle of friends is limited by theborder barriers of the circle of friends On the whole there isa large gap between the speed of propagation and the rangeof communication compared with the public account

e WeChat group has special properties e WeChatgroup can take into account both strong and weak rela-tionships for propagation that is members in the WeChatgroup may not be known or trusted and members of theWeChat group may or may not be influential is can breakthe barriers of the circle of friends based on strong rela-tionships so that the spread of epidemic-related informationis wider and faster e degree to which the recipient of theinformation believes the information is based on thesefactors

In summary this article integrates these three elementsinto a ldquoSupernetworkrdquo of WeChat epidemic informationdissemination systems based on the association between thepublic accounts common WeChat users and WeChatgroups referred to as the WeChat epidemic informationdissemination Supernetwork

21 SupernetworkModeling ofWeChat Epidemic InformationDissemination From the previous analysis we can see thatthere are three types of epidemic information disseminationnetworks in Figure 1

(1) e P-P common WeChat user relationship net-workrsquos nodes are common WeChat users e net-work can be expressed as Gp (P EPminusP) whereP p1 p2 pb1113864 1113865 is a set of commonWeChat userrelationship network members EPminusP (pi1113864 pj) | pi

pj isin P is a set of edges and (pi pj) is a commonWeChat user ere is an association between pi andpj

(2) e M-M WeChat group network is the networkconstructed by the WeChat group e nodes areWeChat groups and the edges represent the asso-ciation between WeChat groups Its model isGm (M EMminusM) M m1 m2 ma1113864 1113865 is a col-lection of WeChat groups EMminusM (mi1113864 mj) | mi

mj isinM is a collection of association relationshipsbetween WeChat groups and edge (mi mj) indi-cates that there is an association between WeChatgroups mi and mj

(3) e I-I WeChat public account network is formedbetween public accounts e node is a WeChatpublic account e network can be described asGi (I EIminusI) I i1 i2 ic1113864 1113865 is a collection of publicaccounts and EIminusI (ii ij) | ii ij isin I1113966 1113967 is a collection ofassociations between public accounts (ii ij) indicatesthat there is an association between ii and ij

e following mapping relationships exist between thethree networks

(1) e mapping between WeChat general users andWeChat public accounts refers to which ordinaryWeChat users pay attention to which public accountsand which common WeChat users follow whichpublic accounts

(2) e mapping between WeChat groups and publicaccounts refers to which public accounts are asso-ciated with which WeChat groups

(3) e mapping between ordinary WeChat users andWeChat groups refers to which ordinary WeChatusers join or are added to which WeChat groupswhich WeChat groups are associated and whichWeChat groups include which ordinary WeChatusers

According to the mapping relationship described abovea mapping relationship can be established betweenGi Gp Gm nodes so that they are integrated together toconstruct a Supernetwork with three types of nodes especific approach is based on the three networks that alreadyexist and the mapping relationship between different typesof nodes is also added as an edge thereby integrating threedifferent types of networks together is process can beexpressed as follows

Let pi isin P ij isin I and ml isinM respectively representany node of the WeChat general user association networkWeChat public account network and WeChat group as-sociation networke Boolean variables ϕ(pi ij) φ(pi ml)and c(ij ml) indicate whether the different types of nodes

Mathematical Problems in Engineering 3

are related where the value 1 is time-dependent and 0 is notrelevant us

WEIDSN f Gi Gp Gm1113872 1113873

Gi + Gp + Gm + Epminusi + Epminusm + Emminusi

I P M EIminusI EPminusP EMminusM Epminusi Epminusm Emminusi1113872 1113873

(1)

here Epminusi (pi ij) |ϕ(pi ij) 11113966 1113967 represents a set of as-sociation relationships between P and I nodes Epminusm

(pi1113864 ml) |φ(pi ml) 1 represents a collection of associ-ation relationships between P and M nodes and Emminusi

(ij1113966 ml) | c(ij ml) 1 represents a collection of associa-tions between I and M nodes

It can be seen that theWeChat Supernetworkmodel is anintegration of three epidemic information disseminationnetworks which reveals the complex composition andstructural form of epidemic information dissemination inWeChat

22 Construction of Adjacency Matrix and Network IntuitiveGraphofWeChatEpidemic InformationSupernetworkModelAt this stage we can use network analysis tools to measurevarious parameters of network analysis and network rela-tionship characterization software can draw network graphsfor intuitive comparison

Figure 1 is a schematic diagram of a three-networkintegration Supernetwork of a WeChat epidemic informa-tion dissemination system e figure is divided into threelayers e top layer is the WeChat group network enetwork members are WeChat groups ere may be as-sociations between the network members and the networkmembers may also be associated with the members of theother two layers mi represents the nodes in this layernetwork e middle layer of the network is the ordinaryWeChat user relationship network e network membersare ordinary WeChat users ere may be associations be-tween the network members and the network members mayalso be associated with members of the other two layers pi

represents nodes in this layer of the network e bottomlayer is the WeChat official account network e network

members are WeChat official accounts ere may be as-sociations between the network members and the networkmembers may also be associated with members of the othertwo layers of networks ii represents nodes in this layernetwork Figure 1 is a schematic diagram of a WeChatepidemic information dissemination Supernetwork inwhich ordinaryWeChat user p2 joinsWeChat groupm1 andordinary WeChat users p3 and p4 join WeChat groups m4and m5 After joining the WeChat groups m3 and m4 theordinary WeChat user p1 is added to the three WeChatgroups m2 m4 and m5 at the same time and the ordinaryWeChat user p5 is temporarily not added to any WeChatgroup WeChat groups m1 m2 and m5 are associated withthe public account network ordinary WeChat user p2 paysattention to the public accounts i2 and i3 ordinary user p3pays attention to the public accounts i1 i2 and i5 at the sametime and ordinary user p4 pays attention to the publicaccount i4 along with ordinary user p5 After paying at-tention to the public accounts i2 i4 and i5 the ordinaryWeChat user p1 does not follow anyWeChat public accountfor the time being Taking theWeChat epidemic informationdissemination Supernetwork as an example the boundary ofthe epidemic information dissemination subnetwork of theWeChat epidemic information dissemination system isdetermined and its many network nodes and their asso-ciations are established e rules for constructing the as-sociation relationship of network nodes are as follows If thetwo nodes in the schematic diagram of theWeChat epidemicinformation dissemination Supernetwork are connectedthey are marked as 1 otherwise they are marked as 0 Usingnetwork analysis software the adjacency matrix of theWeChat epidemic information dissemination Supernetworkcan be constructed as shown in Figure 2

At the same time the corresponding network analysisstandard file can be generated and imported into thespecified network relationship characterization softwarewhich can be processed according to specific needs orpurposes and used to then construct a network intuitive mapof the WeChat epidemic information disseminationSupernetwork as shown in Figure 3

e representative WeChat epidemic information dis-semination Supernetwork model outlined in this paper is a

m1

m2

m3m4 m5

p1p2

p3 p4

p5

i1

i2i3

i4

i5

Ordinary user relationship

network (including

WeChat friend circle)

WeChat group

network

WeChat public

account network

Figure 1 WeChat epidemic information dissemination Supernetwork

4 Mathematical Problems in Engineering

network of three different types of epidemic informationdissemination networks including the public account net-work WeChat group network and common WeChat userrelationship network e Supernetwork model containsthree relatively active and representative information carrierelements in the WeChat epidemic information dissemina-tion system such as WeChat public accounts WeChatgroups common WeChat users and their complex asso-ciations Compared with the epidemic information dis-semination network composed of similar nodes and theirassociations the Supernetwork model can better reflect thecomplex composition and structural form of the WeChatepidemic information dissemination network system so itcan be more accurate comprehensive and provide more in-depth WeChat epidemic information e communicationnetwork system conducts research and analysis lays afoundation and provides help for the management andguidance of subsequent WeChat epidemic informationdissemination

3 Identification of Key Nodes in WeChatEpidemic InformationDissemination Supernetwork

An important part of guiding the spread of epidemic-relatedinformation in WeChat is to first identify the key nodes inthe spread of WeChat epidemic information ese

important related nodes largely affect the spread of epi-demic-related information in WeChat

31 Traditional Key Node Identification Method e degreecentricity method in network analysis theory is the mainmethod for identifying key nodes in a network e formulais as follows

CD ni( 1113857 d ni( 1113857 1113944j

Xij 1113944j

Xji

CDprime ni( 1113857

d ni( 1113857

g minus 1

(2)

e value of Xji is 1 or 0 indicating whether node j isassociated with node i and g is the number of nodes in thenetwork In the network because the number of nodes ineach network is different and the number of large networknodes is large the standardization process must be dividedby the maximum possible number of relationships of a nodein the network that is g minus 1 relationships [19 20] Of coursein addition to the degree centrality method there are manymethods for identifying network central nodes but thedegree centrality method is relatively simple and straight-forward and the application scenarios of this method arealso broader with fewer restrictions on implementation [21]e network analysis tool was used to calculate the degreecentrality of all nodes in the Supernetwork as shown inFigure 3 and the system calculation results are as follows

00000000

0000

0000 0000 0000 0000 0000

00000000 00000000

00000000

0000

1000 00000000 0000 0000 0000 0000 0000 0000 000000000000 0000 0000 0000 0000 0000 0000 0000 0000 0000

0000 0000 0000 0000 0000 00000000 0000 00000000 0000 0000 0000 0000

0000000000000000 00000000

0000 0000000000000000

00000000

0000 0000 0000 000000000000 0000

000000000000 00000000

00000000

0000 0000 0000 00000000 0000 0000 0000

00000000

0000 0000 0000 00000000

00000000 0000 0000

0000 0000 0000 0000 0000 0000000000000000 0000 0000 0000

0000 0000 0000 00000000 0000

0000 0000 00000000 0000 0000 0000

0000 0000 0000 0000

0000 00000000

0000 0000 00000000 0000

0000 0000

1000 0000 0000 1000 0000 0000 000000001000

10001000

1000

1000

1000

10001000

10001000 1000 1000

1000 1000

1000

1000 0000 0000 0000 0000 00001000 0000 1000 1000 1000

1000

10001000 10001000

10001000

1000

10001000 1000 1000

1000

1000 10001000 1000 1000 1000

10001000 1000 1000

10001000 1000

1000 1000 10001000

100010001000 1000

10001000

1000 1000

1000 1000 10001000

1000 1000 10001000

1000

10001000

0000 0000123456789101112131415

m1m2m3m4m5

p3p4

p1p2

p5

i3i4i5

i2i1

1000

0000 1000 00000000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15m1 m2 m3 m4 m5 p1 p2 p3 p4 p5 i1 i2 i3 i4 i5

Figure 2 e adjacency matrix of the WeChat epidemic information Supernetwork

m1

m2

m3

m4

i1

i2

i3

i4

i5

p4

p5

p3

p1

m5

p2

Figure 3 Intuitive map of the WeChat epidemic information dissemination Supernetwork

Mathematical Problems in Engineering 5

From the results in the above figure we can see that thedegree of centrality of node p3 is 9 the degree of centrality ofp4 is 7 and the standardization of the two nodes is 064286and 05 respectively It can be seen that the p3 node and thep4 node are relatively important During the spread ofWeChat epidemic-related information monitoring andguiding these two nodes has a great impact on the overallinformation spread

32 Key Node Recognition Method Based on WeChatSupernetwork Degree centrality is currently one of the mostcommonly used key node identification methods but itsapplication in a Supernetwork has deficiencies e degreecentrality calculation here does not distinguish which subneteach node belongs to in the Supernetwork there is nodistinction between the relationships between nodes andthere is no difference between the relationships betweensubnets Accordingly this method cannot reflect the con-nection status of a node in the subnet to which it belongsnor can it reflect the propagation ability of the node in thesubnet to which it belongs similarly in the current situationthis method also fails to reflect the connection status of anode between subnetworks and it fails to measure thepropagation ability of the node between subnetworks Re-ferring to Figures 3 and 4 for example the i1 node has adegree of centrality of

CD(i1) d(i1) 1113944j

Xij 1113944j

Xji 3 (3)

And the m3 node has a degree of centrality of

CD(m3) d(m3) 1113944j

Xij 1113944j

Xji 4 (4)

According to the formula

CDprime ni( 1113857

d ni( 1113857

g minus 1 (5)

e standardized degree of centrality of i1 can be ob-tained as

CDprime (i1)

d(i1)

g minus 1 021429 (6)

And the standardized degree of centrality of node m3 is

CDprime (m3)

d(m3)

g minus 1 028571 (7)

us node i1 is not as important as m3 but in theprocess of epidemic information propagation in WeChat inthe Supernetwork i1 is associated with three unary subnetswhile m3 is only associated with the M-M network and P-Pnetwork and is not directly connected to the I-I networkFrom this perspective i1 is more important than m3 espread of epidemic information in WeChat has uniquefeatures For example the ability of ordinary WeChat usersto spread information in the circle of friends is related to thenumber of their friends the ability of the public account tospread information in WeChat is related to the number of

fans and the ability to spread information inWeChat groupsand the number of WeChat group members is related enodes with strong propagation ability are more importantand the identificationmethods of these key nodes inWeChatneed to be rebuilt

In order to avoid the above deficiencies this paperproposes a new comprehensive method for identifying keynodes in WeChat epidemic information disseminationbased on a Supernetwork part of which is based on animprovement of the decision method proposed previously[13] and the other part is mainly constructed based on thecharacteristics of the spread of epidemic information inWeChat e new method is briefly described as follows

Let ni be any node in the Supernetwork QCD(ni)

represents the degree of centrality of ni in the entireSupernetwork and ZCD(ni) is the degree of centrality of ni

in the unary subnet to which it belongs

(1) Step 1 Calculate and compare the degree of cen-trality of each node in the entire Supernetwork

(2) Step 2 Calculate and compare the degree centralityof all nodes in the M-P binary subnetwork and theI-P binary subnetwork in the M-P binary subnet-work and I-P binary subnetwork to which theybelong

(3) Step 3 Calculate and compare the degree centralityof all the individuals in the entire Supernetworksystem in the subunit networks to which they belong

(4) Step 4 Calculate and compare the internetworkpropagation capabilities of each node in the subnet ofa unitary network in the Supernetwork Let LZS(ni)

be the number of unitary subnetworks connected bynode ni and ZJBS(ni) the edges of node ni betweenthe unitary subnetworks e number can be ob-tained from the above analysisZJBS(ni) QCD(ni) minus ZCD(ni) the network prop-agation ability of the node ni in the Supernetwork isexpressed by ZJCN(ni) and the calculation andcomparison methods are as follows

Select Case LZS(A)

Case ISgt LZS(B)

ZJCN(A)gtZJCN(B)

Case ISlt LZS(B)

ZJCN(A)ltZJCN(B)

Case IS LZS(B)

Select Case ZJBS(A)

Case ISgtZJBS(B)

ZJCN(A)gtZJCN(B)

Case ISltZJBS(B)

ZJCN(A)ltZJCN(B)

Case IS ZJBS(B)

ZJCN(A) ZJCN(B)

End SelectEnd Select

6 Mathematical Problems in Engineering

(5) Step 5 Calculate and compare the internetworkpropagation capability ZJCNJ(ni) between theM-type nodes in the M-P binary subnetwork and theI-type nodes in the I-P binary subnetwork under thecorresponding binary subnetwork view LetJMminusPCD(ni) represent the degree of centrality of ni inthe M-P binary subnetwork to which it belongs andlet JIminusPCD(ni) represent the degree of centrality of ni

in the I-P binary subnetwork to which it belongs andthe calculation method of ZJCNJ(ni) is as followsSelect Case ni

Case IS isinM

ZJCNJ(ni) JMminusPCD(ni) minus ZCD(ni)

Case IS isin I

ZJCNJ(ni) JIminusPCD(ni) minus ZCD(ni)

End Select(6) Combining the results of the above steps key nodes

are identified

In the above steps Step 2 prepares for the calculation andcomparison of the number of fans of the public account andthe number of members in the WeChat group is determinedin Step 5 Step 3 the calculation result can also obtain thenumber of friends of ordinary WeChat users in the circle offriends e circle of friends is one of the main channels forordinary users to disseminate information in WeChat enumber of friends in the circle of friends is an importantcriterion for identifying the ability of ordinaryWeChat usersto disseminate information Step 4 compares the unarysubnet internetwork propagation capabilities of each node inthe Supernetwork view by the number of unary subnetworksconnected by the nodes and the number of nodes connectedbetween the unary subnetworks A ranking table was createdshowing the strengths and weaknesses of the unary subnetrsquosinternetwork spreading ability under the Supernetworkvision Among them QCD(ni) can be obtained by Step 1ZCD(ni) can be obtained by Step 3 and the individualrsquosZJBS(ni) can be obtained by the difference between QCD(ni)

and ZCD(ni) of an individual Firstly it is judged based onthe number of unary subnetworks connected to the node

e number of unary subnetworks connected to node A isgreater than the number of unary subnetworks connected tonode B which indicates that the internetwork communi-cation capability of node A is stronger than that of node B Ifthe number of unary subnetworks connected to node A isless than the number of unary subnetworks connected tonode B it indicates that the internetwork propagation ca-pability of node A between unary subnetworks is weakerthan that of node B If the number of unary subnetworksconnected to node A is the same as the number of unarysubnetworks connected to node B further judgments needto be made based on the number of edges between the unarysubnetworks of nodes Step 5 is mainly based on the cal-culation results of Step 2 and Step 3 and calculates andcompares the number of fans of the public account and thenumber of members of the WeChat group in the WeChatSupernetwork e information dissemination ability ofnodes is measured to provide a reference for the identifi-cation of key nodes is step calculates the internetworkpropagation capability between theM-type nodes in theM-Pbinary subnetwork and the I-type nodes in the I-P binarysubnetwork from the binary subnetwork perspective

Taking the example shown in Figure 3 for verificationand analysis

(1) Step 1 e calculation result is shown in Figure 4(2) Step 2 e screenshots of the system calculation

results are shown in Figures 5 and 6(3) Step 3 e result is shown in Figure 7(4) Step 4 e results are shown in Table 1(5) Combining the comparison and calculation results

of Step 2 and Figures 5 and 6 with the comparisonand calculation results of Step 3 and Figure 7 thecalculation and comparison results of this step areshown in Tables 2 and 3

(6) From the perspective of intranetwork propagationFigure 7 shows that the degree of centrality of i3 i4and i5 in the I-I network is the same and the highestand the propagation ability of i3 i4 and i5 in thenetwork is also the strongest Nodesm1m2m3 and

8 9000 64286 01229 7000 50000 00954 6000

50005000

500050005000500040004000300030003000

42857 008110 35714

35714

35714357143571435714

12 i2671215 0068

006800680068

00685000 35714 0068

0068

3 2857128571 0054

00541413

2142921429

21429115 0041

00410041

Degree1

NrmDegree2

Share3

p3p4m4p5

p1p2m1m2

i3i4

i5

i1m5

m3

Figure 4 e degree of centrality of all nodes in the WeChat epidemic information Supernetwork

Mathematical Problems in Engineering 7

m4 have strong propagation capabilities in the M-Mnetwork In the P-P network p3 and p4 are thestrongest nodes in the network From the perspectiveof internetwork propagation Table 1 shows that thenumber of subnetworks connected by nodes p3 andi2 is larger and the number of interconnected edgesbetween networks is also larger so their internet-work propagation capabilities are stronger edegree centrality value of such nodes may not be

large but its influence on the propagation effect isoften large which is worthy of attention It can alsobe seen from Table 1 that although m3 has thestrongest propagation capability in the M-M net-work and i1 has the weakest propagation capabilityin the I-I network in Figure 7 from the perspective ofinternetwork propagation i1 connects three subnetsthere are 2 internetwork edges m3 only connects 2subnets and there is only 1 internetwork edge so i1

3 7000 77778 01754 5000

50004000400040004000300020002000

55556 01255 55556 01252 44444

444444444444444333332222222222

01007 010010 01009 01008 00751 00506 0050

Degree1

NrmDegree2

Share3

p3p4p5p2i2i5i4i3p1i1

Figure 5 e degree of centrality of all nodes in the I-P network

6000600060005000400040004000300020002000

666676666766667

014301430143

55556 0119444444444444444

009500950095

33333 007122222 0048

8 p34 m49 p46 p12 m21 m13 m37 p25 m510 p5 22222 0048

Degree1

NrmDegree2

Share3

Figure 6 e degree of centrality of all nodes in the M-P network

12345

34125

34521

m1m2m3m4m5

Degree1

30003000300030000000

NrmDegree2

0000

750007500075000

75000

Share3

0000

0250025002500250

p3p4p1p2p5

Degree1

40004000200020002000

2000

20002000

NrmDegree2

100000100000500005000050000

500005000050000

Share3

Degree1

NrmDegree2

Share3

02860286014301430143

10001000 25000

25000

02500250025001250125

i3i4i5i2i1

Figure 7 e degree of centrality of each node in the unary subnet to which it belongs

8 Mathematical Problems in Engineering

is slightly better than m3 in terms of internetworkcommunication capability From the perspective ofthe spread of epidemic-related information inWeChat Figure 7 shows that p3 and p4 have a strongability to spread epidemic-related information in theWeChat circle of friends Under the same conditionsthe spread of epidemic-related information of thesetwo ordinary user nodes is faster e spreadingrange is wide Table 2 shows that m4 has a strongspreading capability in WeChat group nodes Underthe same conditions the information spreadingspeed of this WeChat group node is faster and thespreading range is wider Table 3 shows i2 in thepublic account category e dissemination capa-bility of the node is strong Under the same con-ditions the public information nodersquos epidemic-related information spreads faster more widely Toguide the dissemination of epidemic-related infor-mation in WeChat it is best to guide the

abovementioned WeChat nodes with a strong abilityto disseminate epidemic-related information

e new method also identifies the importance of or-dinary WeChat users WeChat groups and official accountsfrom the perspective of information diffusion based on theparticularity of the spread of WeChat epidemic-relatedinformation in order to be more comprehensive andreasonable

4 Conclusions

is article mainly concerns the model construction and keynode identification of the WeChat epidemic-related infor-mation dissemination Supernetwork e identificationmethod can be roughly divided into two parts One part isbased on the improvement of the decision method proposedpreviously [13] and the other part of it is mainly based onthe characteristics of the spread of information related to the

Table 1 Sequence table of nodersquos internetwork epidemic information dissemination ability

Node Number of unary subnets associated Number of relationshipsp3 3 5i2 3 4p2 3 3p4 3 3i5 3 3m1 3 2i1 3 2m2 3 2m5 2 3p1 2 3m4 2 3p5 2 3i4 2 2m3 2 1i3 2 1

Table 3 Sorting table of the spreading capacity of epidemic information in WeChat for Class I nodes

Node Degree of centralitywithin the I-P network

Degree of centrality withinthe I-I network

Important indicators of WeChatepidemic information dissemination capability

i2 4 1 3i4 4 2 2i5 4 2 2i3 3 2 1i1 2 1 1

Table 2 Sorting table of M-type nodesrsquo epidemic information dissemination capability in WeChat

Node Degree of centralitywithin the M-P network

Degree centrality withinthe M-M network

Important indicators of WeChatepidemic information dissemination capability

m4 6 3 3m5 2 0 2m1 4 3 1m2 4 3 1m3 4 3 1

Mathematical Problems in Engineering 9

epidemic in WeChat e Supernetwork model of WeChatepidemic information dissemination and the correspondingkey node identification method constructed in this study arethe initial attempts to research the information dissemi-nation of epidemic-related information in WeChat

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

PengWu and Di Zhao contributed to the design of the studyPeng Wu gave the main idea of the manuscript wrote thefirst draft and performed the design of figures All authorscontributed to the manuscript revision and read and ap-proved the submitted version

Acknowledgments

is work was supported by the National Social ScienceFund Project (18BGL238) China the China PostdoctoralScience Foundation Special Funding Project (2018T110724)China the Chinese Postdoctoral Science Fund GeneralSupport Project (2016M602236) China and the HenanPhilosophy and Social Science Planning Project(2017BJJ021) and Key Research Project of Teacher Educa-tion Curriculum Reform in Henan Province (2018-JSJYZD-008) China

References

[1] Science Net ldquoMining social network opinion leadersrdquo 2020httpblogsciencenetcnhomephpmodspaceampuid3075ampdoblogampid466991

[2] Surging News ldquoe 2019 WeChat annual data report is outrdquo2020 httpswwwthepapercnnewsDetail_forward_5480482

[3] L L Liu ldquoResearch on new coronary pneumonia epidemicreports from the perspective of the frameworkrdquo JournalismLover vol 5 pp 17ndash21 2020

[4] Z Deng X J Liu and Z D Kang ldquoResearch on the publicopinion propaganda and ideological education function ofuniversity new media in the prevention and control of majorepidemicsrdquo Studies in Ideological Education no 3 pp 38ndash432020

[5] Y S Chen ldquoResearch on spreading and governance of in-ternet rumors on public health emergencyrdquo E-Governmentno 6 pp 2ndash11 2020

[6] B J Wan C Guo Z Zhao et al ldquoCharacteristics and risksreflections of ldquoanti-epidemic fitness messagesrdquo delivered byWeChat during the COVID-19 epidemicrdquo Journal of XirsquoanPhysical Education University vol 37 no 3 pp 267ndash2752020

[7] Y Lu and L Zhang ldquoSocial media WeChat infers the de-velopment trend of COVID-19rdquo Journal of Infection no 81pp 82-83 2020

[8] A Nagurney and J Dong SupernetworksDecision-Making forthe Information Age Edward Elgar Publishing CheltenhamUK 2002

[9] Z P Wang and Z T Wang Supernetwork eory and itsApplication Science Press Beijing China 2008

[10] A Nagurney ldquoOptimal supply chain network design andredesign at minimal total cost and with demand satisfactionrdquoInternational Journal of Production Economics vol 128 no 1pp 200ndash208 2010

[11] A Nagurney M Yu and Q Qiang ldquoSupply chain networkdesign for critical needs with outsourcingrdquo Papers in RegionalScience vol 90 no 1 pp 123ndash142 2011

[12] L Zhu and J Cao ldquoSupernetwork optimization of emergencyresources allocation under disaster riskrdquo Chinese Journal ofManagement Science vol 20 no 6 pp 141ndash148 2012

[13] P Wu and H S Wang ldquoModeling of information dissemi-nation supernetwork in the emergencies and determination ofthe important nodes in the supernetworkrdquo Journal of theChina Society for Scientific and Technical Information vol 37no 7 pp 722ndash729 2012

[14] Y J Xi Y Z Dang and K J Liao ldquoKnowledge supernetworkmodel and its application in organizational knowledge sys-temsrdquo Journal of Management Sciences in China vol 12 no 3pp 12ndash21 2009

[15] P Wu H S Wang Y Li et al ldquoJudgment of importantcontrol nodes in the information dissemination super-net-work of emergencyrdquo Library and Information Service vol 57no 1 pp 112ndash116 2013

[16] Y Yu Research on Knowledge Supernetwork in OrganizationalKnowledge Management Dalian University of TechnologyDalian China 2009

[17] J L Segovia-juarez S Colombano and D KirschnerldquoIdentifying DNA splice sites using hypernetworks with ar-tificial molecular evolutionrdquo Biosystems vol 87 no 2-3pp 117ndash124 2007

[18] Z T Wang ldquoReflection on supernetworkrdquo Journal of Uni-versity of Shanghai for Science and Technology vol 33 no 3pp 229ndash237 2011

[19] J-B Liu J Cao A Alofi A AL-Mazrooei and A ElaiwldquoApplications of laplacian spectra for n-prism networksrdquoNeurocomputing vol 198 pp 69ndash73 2016

[20] J D Luo Lecture Notes on Social Network Analysis SocialSciences Academic Press Beijing China 2nd edition 2010

[21] S Hayat S Wang and J-B Liu ldquoValency-based topologicaldescriptors of chemical networks and their applicationsrdquoApplied Mathematical Modelling vol 60 pp 164ndash178 2018

10 Mathematical Problems in Engineering

the study of the network using the relationship between theoutside and the network and the study of overall perfor-mance e modeling work of this article is mainly inspiredand helped by some research results in this area Researchbased on hypergraphs [17] is considered to be another moreimportant research direction It is mostly used to solve theproblem of different textures between edges and nodes innetwork research Hypergraphs are used to describe thesystem and study the statistical characteristics of the net-worke research on Supernetworks has developed rapidlyand its application fields are also relatively wide such asknowledge management supply chains transportation fi-nancial management advertising e-commerce biology andorganization and cooperation [18] However Supernetworktheory andmethods are rarely applied to the field ofWeChatepidemic information dissemination

WeChat public accounts common WeChat users andWeChat groups are the main outlets through which epi-demic information is spread in WeChat e public accountmainly disseminates information through the weak rela-tionship between the public account and the fanse publicaccount and the fans form a star network Relativelyspeaking the communication speed is fast and the spread iswide but the audience trusts the public account to releaseinformation though this is not the most trusted source ofinformation

e ordinary users of WeChat mainly spread informa-tion through the strong relationship between ordinary usersrsquofriends e information publisher and information receiverin the circle of friends also form a star network Because ofthe relationships between acquaintances the informationposted in the circle of friends is related to the circle offriends Members tend to believe this information more butthe information in the circle of friends is limited by theborder barriers of the circle of friends On the whole there isa large gap between the speed of propagation and the rangeof communication compared with the public account

e WeChat group has special properties e WeChatgroup can take into account both strong and weak rela-tionships for propagation that is members in the WeChatgroup may not be known or trusted and members of theWeChat group may or may not be influential is can breakthe barriers of the circle of friends based on strong rela-tionships so that the spread of epidemic-related informationis wider and faster e degree to which the recipient of theinformation believes the information is based on thesefactors

In summary this article integrates these three elementsinto a ldquoSupernetworkrdquo of WeChat epidemic informationdissemination systems based on the association between thepublic accounts common WeChat users and WeChatgroups referred to as the WeChat epidemic informationdissemination Supernetwork

21 SupernetworkModeling ofWeChat Epidemic InformationDissemination From the previous analysis we can see thatthere are three types of epidemic information disseminationnetworks in Figure 1

(1) e P-P common WeChat user relationship net-workrsquos nodes are common WeChat users e net-work can be expressed as Gp (P EPminusP) whereP p1 p2 pb1113864 1113865 is a set of commonWeChat userrelationship network members EPminusP (pi1113864 pj) | pi

pj isin P is a set of edges and (pi pj) is a commonWeChat user ere is an association between pi andpj

(2) e M-M WeChat group network is the networkconstructed by the WeChat group e nodes areWeChat groups and the edges represent the asso-ciation between WeChat groups Its model isGm (M EMminusM) M m1 m2 ma1113864 1113865 is a col-lection of WeChat groups EMminusM (mi1113864 mj) | mi

mj isinM is a collection of association relationshipsbetween WeChat groups and edge (mi mj) indi-cates that there is an association between WeChatgroups mi and mj

(3) e I-I WeChat public account network is formedbetween public accounts e node is a WeChatpublic account e network can be described asGi (I EIminusI) I i1 i2 ic1113864 1113865 is a collection of publicaccounts and EIminusI (ii ij) | ii ij isin I1113966 1113967 is a collection ofassociations between public accounts (ii ij) indicatesthat there is an association between ii and ij

e following mapping relationships exist between thethree networks

(1) e mapping between WeChat general users andWeChat public accounts refers to which ordinaryWeChat users pay attention to which public accountsand which common WeChat users follow whichpublic accounts

(2) e mapping between WeChat groups and publicaccounts refers to which public accounts are asso-ciated with which WeChat groups

(3) e mapping between ordinary WeChat users andWeChat groups refers to which ordinary WeChatusers join or are added to which WeChat groupswhich WeChat groups are associated and whichWeChat groups include which ordinary WeChatusers

According to the mapping relationship described abovea mapping relationship can be established betweenGi Gp Gm nodes so that they are integrated together toconstruct a Supernetwork with three types of nodes especific approach is based on the three networks that alreadyexist and the mapping relationship between different typesof nodes is also added as an edge thereby integrating threedifferent types of networks together is process can beexpressed as follows

Let pi isin P ij isin I and ml isinM respectively representany node of the WeChat general user association networkWeChat public account network and WeChat group as-sociation networke Boolean variables ϕ(pi ij) φ(pi ml)and c(ij ml) indicate whether the different types of nodes

Mathematical Problems in Engineering 3

are related where the value 1 is time-dependent and 0 is notrelevant us

WEIDSN f Gi Gp Gm1113872 1113873

Gi + Gp + Gm + Epminusi + Epminusm + Emminusi

I P M EIminusI EPminusP EMminusM Epminusi Epminusm Emminusi1113872 1113873

(1)

here Epminusi (pi ij) |ϕ(pi ij) 11113966 1113967 represents a set of as-sociation relationships between P and I nodes Epminusm

(pi1113864 ml) |φ(pi ml) 1 represents a collection of associ-ation relationships between P and M nodes and Emminusi

(ij1113966 ml) | c(ij ml) 1 represents a collection of associa-tions between I and M nodes

It can be seen that theWeChat Supernetworkmodel is anintegration of three epidemic information disseminationnetworks which reveals the complex composition andstructural form of epidemic information dissemination inWeChat

22 Construction of Adjacency Matrix and Network IntuitiveGraphofWeChatEpidemic InformationSupernetworkModelAt this stage we can use network analysis tools to measurevarious parameters of network analysis and network rela-tionship characterization software can draw network graphsfor intuitive comparison

Figure 1 is a schematic diagram of a three-networkintegration Supernetwork of a WeChat epidemic informa-tion dissemination system e figure is divided into threelayers e top layer is the WeChat group network enetwork members are WeChat groups ere may be as-sociations between the network members and the networkmembers may also be associated with the members of theother two layers mi represents the nodes in this layernetwork e middle layer of the network is the ordinaryWeChat user relationship network e network membersare ordinary WeChat users ere may be associations be-tween the network members and the network members mayalso be associated with members of the other two layers pi

represents nodes in this layer of the network e bottomlayer is the WeChat official account network e network

members are WeChat official accounts ere may be as-sociations between the network members and the networkmembers may also be associated with members of the othertwo layers of networks ii represents nodes in this layernetwork Figure 1 is a schematic diagram of a WeChatepidemic information dissemination Supernetwork inwhich ordinaryWeChat user p2 joinsWeChat groupm1 andordinary WeChat users p3 and p4 join WeChat groups m4and m5 After joining the WeChat groups m3 and m4 theordinary WeChat user p1 is added to the three WeChatgroups m2 m4 and m5 at the same time and the ordinaryWeChat user p5 is temporarily not added to any WeChatgroup WeChat groups m1 m2 and m5 are associated withthe public account network ordinary WeChat user p2 paysattention to the public accounts i2 and i3 ordinary user p3pays attention to the public accounts i1 i2 and i5 at the sametime and ordinary user p4 pays attention to the publicaccount i4 along with ordinary user p5 After paying at-tention to the public accounts i2 i4 and i5 the ordinaryWeChat user p1 does not follow anyWeChat public accountfor the time being Taking theWeChat epidemic informationdissemination Supernetwork as an example the boundary ofthe epidemic information dissemination subnetwork of theWeChat epidemic information dissemination system isdetermined and its many network nodes and their asso-ciations are established e rules for constructing the as-sociation relationship of network nodes are as follows If thetwo nodes in the schematic diagram of theWeChat epidemicinformation dissemination Supernetwork are connectedthey are marked as 1 otherwise they are marked as 0 Usingnetwork analysis software the adjacency matrix of theWeChat epidemic information dissemination Supernetworkcan be constructed as shown in Figure 2

At the same time the corresponding network analysisstandard file can be generated and imported into thespecified network relationship characterization softwarewhich can be processed according to specific needs orpurposes and used to then construct a network intuitive mapof the WeChat epidemic information disseminationSupernetwork as shown in Figure 3

e representative WeChat epidemic information dis-semination Supernetwork model outlined in this paper is a

m1

m2

m3m4 m5

p1p2

p3 p4

p5

i1

i2i3

i4

i5

Ordinary user relationship

network (including

WeChat friend circle)

WeChat group

network

WeChat public

account network

Figure 1 WeChat epidemic information dissemination Supernetwork

4 Mathematical Problems in Engineering

network of three different types of epidemic informationdissemination networks including the public account net-work WeChat group network and common WeChat userrelationship network e Supernetwork model containsthree relatively active and representative information carrierelements in the WeChat epidemic information dissemina-tion system such as WeChat public accounts WeChatgroups common WeChat users and their complex asso-ciations Compared with the epidemic information dis-semination network composed of similar nodes and theirassociations the Supernetwork model can better reflect thecomplex composition and structural form of the WeChatepidemic information dissemination network system so itcan be more accurate comprehensive and provide more in-depth WeChat epidemic information e communicationnetwork system conducts research and analysis lays afoundation and provides help for the management andguidance of subsequent WeChat epidemic informationdissemination

3 Identification of Key Nodes in WeChatEpidemic InformationDissemination Supernetwork

An important part of guiding the spread of epidemic-relatedinformation in WeChat is to first identify the key nodes inthe spread of WeChat epidemic information ese

important related nodes largely affect the spread of epi-demic-related information in WeChat

31 Traditional Key Node Identification Method e degreecentricity method in network analysis theory is the mainmethod for identifying key nodes in a network e formulais as follows

CD ni( 1113857 d ni( 1113857 1113944j

Xij 1113944j

Xji

CDprime ni( 1113857

d ni( 1113857

g minus 1

(2)

e value of Xji is 1 or 0 indicating whether node j isassociated with node i and g is the number of nodes in thenetwork In the network because the number of nodes ineach network is different and the number of large networknodes is large the standardization process must be dividedby the maximum possible number of relationships of a nodein the network that is g minus 1 relationships [19 20] Of coursein addition to the degree centrality method there are manymethods for identifying network central nodes but thedegree centrality method is relatively simple and straight-forward and the application scenarios of this method arealso broader with fewer restrictions on implementation [21]e network analysis tool was used to calculate the degreecentrality of all nodes in the Supernetwork as shown inFigure 3 and the system calculation results are as follows

00000000

0000

0000 0000 0000 0000 0000

00000000 00000000

00000000

0000

1000 00000000 0000 0000 0000 0000 0000 0000 000000000000 0000 0000 0000 0000 0000 0000 0000 0000 0000

0000 0000 0000 0000 0000 00000000 0000 00000000 0000 0000 0000 0000

0000000000000000 00000000

0000 0000000000000000

00000000

0000 0000 0000 000000000000 0000

000000000000 00000000

00000000

0000 0000 0000 00000000 0000 0000 0000

00000000

0000 0000 0000 00000000

00000000 0000 0000

0000 0000 0000 0000 0000 0000000000000000 0000 0000 0000

0000 0000 0000 00000000 0000

0000 0000 00000000 0000 0000 0000

0000 0000 0000 0000

0000 00000000

0000 0000 00000000 0000

0000 0000

1000 0000 0000 1000 0000 0000 000000001000

10001000

1000

1000

1000

10001000

10001000 1000 1000

1000 1000

1000

1000 0000 0000 0000 0000 00001000 0000 1000 1000 1000

1000

10001000 10001000

10001000

1000

10001000 1000 1000

1000

1000 10001000 1000 1000 1000

10001000 1000 1000

10001000 1000

1000 1000 10001000

100010001000 1000

10001000

1000 1000

1000 1000 10001000

1000 1000 10001000

1000

10001000

0000 0000123456789101112131415

m1m2m3m4m5

p3p4

p1p2

p5

i3i4i5

i2i1

1000

0000 1000 00000000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15m1 m2 m3 m4 m5 p1 p2 p3 p4 p5 i1 i2 i3 i4 i5

Figure 2 e adjacency matrix of the WeChat epidemic information Supernetwork

m1

m2

m3

m4

i1

i2

i3

i4

i5

p4

p5

p3

p1

m5

p2

Figure 3 Intuitive map of the WeChat epidemic information dissemination Supernetwork

Mathematical Problems in Engineering 5

From the results in the above figure we can see that thedegree of centrality of node p3 is 9 the degree of centrality ofp4 is 7 and the standardization of the two nodes is 064286and 05 respectively It can be seen that the p3 node and thep4 node are relatively important During the spread ofWeChat epidemic-related information monitoring andguiding these two nodes has a great impact on the overallinformation spread

32 Key Node Recognition Method Based on WeChatSupernetwork Degree centrality is currently one of the mostcommonly used key node identification methods but itsapplication in a Supernetwork has deficiencies e degreecentrality calculation here does not distinguish which subneteach node belongs to in the Supernetwork there is nodistinction between the relationships between nodes andthere is no difference between the relationships betweensubnets Accordingly this method cannot reflect the con-nection status of a node in the subnet to which it belongsnor can it reflect the propagation ability of the node in thesubnet to which it belongs similarly in the current situationthis method also fails to reflect the connection status of anode between subnetworks and it fails to measure thepropagation ability of the node between subnetworks Re-ferring to Figures 3 and 4 for example the i1 node has adegree of centrality of

CD(i1) d(i1) 1113944j

Xij 1113944j

Xji 3 (3)

And the m3 node has a degree of centrality of

CD(m3) d(m3) 1113944j

Xij 1113944j

Xji 4 (4)

According to the formula

CDprime ni( 1113857

d ni( 1113857

g minus 1 (5)

e standardized degree of centrality of i1 can be ob-tained as

CDprime (i1)

d(i1)

g minus 1 021429 (6)

And the standardized degree of centrality of node m3 is

CDprime (m3)

d(m3)

g minus 1 028571 (7)

us node i1 is not as important as m3 but in theprocess of epidemic information propagation in WeChat inthe Supernetwork i1 is associated with three unary subnetswhile m3 is only associated with the M-M network and P-Pnetwork and is not directly connected to the I-I networkFrom this perspective i1 is more important than m3 espread of epidemic information in WeChat has uniquefeatures For example the ability of ordinary WeChat usersto spread information in the circle of friends is related to thenumber of their friends the ability of the public account tospread information in WeChat is related to the number of

fans and the ability to spread information inWeChat groupsand the number of WeChat group members is related enodes with strong propagation ability are more importantand the identificationmethods of these key nodes inWeChatneed to be rebuilt

In order to avoid the above deficiencies this paperproposes a new comprehensive method for identifying keynodes in WeChat epidemic information disseminationbased on a Supernetwork part of which is based on animprovement of the decision method proposed previously[13] and the other part is mainly constructed based on thecharacteristics of the spread of epidemic information inWeChat e new method is briefly described as follows

Let ni be any node in the Supernetwork QCD(ni)

represents the degree of centrality of ni in the entireSupernetwork and ZCD(ni) is the degree of centrality of ni

in the unary subnet to which it belongs

(1) Step 1 Calculate and compare the degree of cen-trality of each node in the entire Supernetwork

(2) Step 2 Calculate and compare the degree centralityof all nodes in the M-P binary subnetwork and theI-P binary subnetwork in the M-P binary subnet-work and I-P binary subnetwork to which theybelong

(3) Step 3 Calculate and compare the degree centralityof all the individuals in the entire Supernetworksystem in the subunit networks to which they belong

(4) Step 4 Calculate and compare the internetworkpropagation capabilities of each node in the subnet ofa unitary network in the Supernetwork Let LZS(ni)

be the number of unitary subnetworks connected bynode ni and ZJBS(ni) the edges of node ni betweenthe unitary subnetworks e number can be ob-tained from the above analysisZJBS(ni) QCD(ni) minus ZCD(ni) the network prop-agation ability of the node ni in the Supernetwork isexpressed by ZJCN(ni) and the calculation andcomparison methods are as follows

Select Case LZS(A)

Case ISgt LZS(B)

ZJCN(A)gtZJCN(B)

Case ISlt LZS(B)

ZJCN(A)ltZJCN(B)

Case IS LZS(B)

Select Case ZJBS(A)

Case ISgtZJBS(B)

ZJCN(A)gtZJCN(B)

Case ISltZJBS(B)

ZJCN(A)ltZJCN(B)

Case IS ZJBS(B)

ZJCN(A) ZJCN(B)

End SelectEnd Select

6 Mathematical Problems in Engineering

(5) Step 5 Calculate and compare the internetworkpropagation capability ZJCNJ(ni) between theM-type nodes in the M-P binary subnetwork and theI-type nodes in the I-P binary subnetwork under thecorresponding binary subnetwork view LetJMminusPCD(ni) represent the degree of centrality of ni inthe M-P binary subnetwork to which it belongs andlet JIminusPCD(ni) represent the degree of centrality of ni

in the I-P binary subnetwork to which it belongs andthe calculation method of ZJCNJ(ni) is as followsSelect Case ni

Case IS isinM

ZJCNJ(ni) JMminusPCD(ni) minus ZCD(ni)

Case IS isin I

ZJCNJ(ni) JIminusPCD(ni) minus ZCD(ni)

End Select(6) Combining the results of the above steps key nodes

are identified

In the above steps Step 2 prepares for the calculation andcomparison of the number of fans of the public account andthe number of members in the WeChat group is determinedin Step 5 Step 3 the calculation result can also obtain thenumber of friends of ordinary WeChat users in the circle offriends e circle of friends is one of the main channels forordinary users to disseminate information in WeChat enumber of friends in the circle of friends is an importantcriterion for identifying the ability of ordinaryWeChat usersto disseminate information Step 4 compares the unarysubnet internetwork propagation capabilities of each node inthe Supernetwork view by the number of unary subnetworksconnected by the nodes and the number of nodes connectedbetween the unary subnetworks A ranking table was createdshowing the strengths and weaknesses of the unary subnetrsquosinternetwork spreading ability under the Supernetworkvision Among them QCD(ni) can be obtained by Step 1ZCD(ni) can be obtained by Step 3 and the individualrsquosZJBS(ni) can be obtained by the difference between QCD(ni)

and ZCD(ni) of an individual Firstly it is judged based onthe number of unary subnetworks connected to the node

e number of unary subnetworks connected to node A isgreater than the number of unary subnetworks connected tonode B which indicates that the internetwork communi-cation capability of node A is stronger than that of node B Ifthe number of unary subnetworks connected to node A isless than the number of unary subnetworks connected tonode B it indicates that the internetwork propagation ca-pability of node A between unary subnetworks is weakerthan that of node B If the number of unary subnetworksconnected to node A is the same as the number of unarysubnetworks connected to node B further judgments needto be made based on the number of edges between the unarysubnetworks of nodes Step 5 is mainly based on the cal-culation results of Step 2 and Step 3 and calculates andcompares the number of fans of the public account and thenumber of members of the WeChat group in the WeChatSupernetwork e information dissemination ability ofnodes is measured to provide a reference for the identifi-cation of key nodes is step calculates the internetworkpropagation capability between theM-type nodes in theM-Pbinary subnetwork and the I-type nodes in the I-P binarysubnetwork from the binary subnetwork perspective

Taking the example shown in Figure 3 for verificationand analysis

(1) Step 1 e calculation result is shown in Figure 4(2) Step 2 e screenshots of the system calculation

results are shown in Figures 5 and 6(3) Step 3 e result is shown in Figure 7(4) Step 4 e results are shown in Table 1(5) Combining the comparison and calculation results

of Step 2 and Figures 5 and 6 with the comparisonand calculation results of Step 3 and Figure 7 thecalculation and comparison results of this step areshown in Tables 2 and 3

(6) From the perspective of intranetwork propagationFigure 7 shows that the degree of centrality of i3 i4and i5 in the I-I network is the same and the highestand the propagation ability of i3 i4 and i5 in thenetwork is also the strongest Nodesm1m2m3 and

8 9000 64286 01229 7000 50000 00954 6000

50005000

500050005000500040004000300030003000

42857 008110 35714

35714

35714357143571435714

12 i2671215 0068

006800680068

00685000 35714 0068

0068

3 2857128571 0054

00541413

2142921429

21429115 0041

00410041

Degree1

NrmDegree2

Share3

p3p4m4p5

p1p2m1m2

i3i4

i5

i1m5

m3

Figure 4 e degree of centrality of all nodes in the WeChat epidemic information Supernetwork

Mathematical Problems in Engineering 7

m4 have strong propagation capabilities in the M-Mnetwork In the P-P network p3 and p4 are thestrongest nodes in the network From the perspectiveof internetwork propagation Table 1 shows that thenumber of subnetworks connected by nodes p3 andi2 is larger and the number of interconnected edgesbetween networks is also larger so their internet-work propagation capabilities are stronger edegree centrality value of such nodes may not be

large but its influence on the propagation effect isoften large which is worthy of attention It can alsobe seen from Table 1 that although m3 has thestrongest propagation capability in the M-M net-work and i1 has the weakest propagation capabilityin the I-I network in Figure 7 from the perspective ofinternetwork propagation i1 connects three subnetsthere are 2 internetwork edges m3 only connects 2subnets and there is only 1 internetwork edge so i1

3 7000 77778 01754 5000

50004000400040004000300020002000

55556 01255 55556 01252 44444

444444444444444333332222222222

01007 010010 01009 01008 00751 00506 0050

Degree1

NrmDegree2

Share3

p3p4p5p2i2i5i4i3p1i1

Figure 5 e degree of centrality of all nodes in the I-P network

6000600060005000400040004000300020002000

666676666766667

014301430143

55556 0119444444444444444

009500950095

33333 007122222 0048

8 p34 m49 p46 p12 m21 m13 m37 p25 m510 p5 22222 0048

Degree1

NrmDegree2

Share3

Figure 6 e degree of centrality of all nodes in the M-P network

12345

34125

34521

m1m2m3m4m5

Degree1

30003000300030000000

NrmDegree2

0000

750007500075000

75000

Share3

0000

0250025002500250

p3p4p1p2p5

Degree1

40004000200020002000

2000

20002000

NrmDegree2

100000100000500005000050000

500005000050000

Share3

Degree1

NrmDegree2

Share3

02860286014301430143

10001000 25000

25000

02500250025001250125

i3i4i5i2i1

Figure 7 e degree of centrality of each node in the unary subnet to which it belongs

8 Mathematical Problems in Engineering

is slightly better than m3 in terms of internetworkcommunication capability From the perspective ofthe spread of epidemic-related information inWeChat Figure 7 shows that p3 and p4 have a strongability to spread epidemic-related information in theWeChat circle of friends Under the same conditionsthe spread of epidemic-related information of thesetwo ordinary user nodes is faster e spreadingrange is wide Table 2 shows that m4 has a strongspreading capability in WeChat group nodes Underthe same conditions the information spreadingspeed of this WeChat group node is faster and thespreading range is wider Table 3 shows i2 in thepublic account category e dissemination capa-bility of the node is strong Under the same con-ditions the public information nodersquos epidemic-related information spreads faster more widely Toguide the dissemination of epidemic-related infor-mation in WeChat it is best to guide the

abovementioned WeChat nodes with a strong abilityto disseminate epidemic-related information

e new method also identifies the importance of or-dinary WeChat users WeChat groups and official accountsfrom the perspective of information diffusion based on theparticularity of the spread of WeChat epidemic-relatedinformation in order to be more comprehensive andreasonable

4 Conclusions

is article mainly concerns the model construction and keynode identification of the WeChat epidemic-related infor-mation dissemination Supernetwork e identificationmethod can be roughly divided into two parts One part isbased on the improvement of the decision method proposedpreviously [13] and the other part of it is mainly based onthe characteristics of the spread of information related to the

Table 1 Sequence table of nodersquos internetwork epidemic information dissemination ability

Node Number of unary subnets associated Number of relationshipsp3 3 5i2 3 4p2 3 3p4 3 3i5 3 3m1 3 2i1 3 2m2 3 2m5 2 3p1 2 3m4 2 3p5 2 3i4 2 2m3 2 1i3 2 1

Table 3 Sorting table of the spreading capacity of epidemic information in WeChat for Class I nodes

Node Degree of centralitywithin the I-P network

Degree of centrality withinthe I-I network

Important indicators of WeChatepidemic information dissemination capability

i2 4 1 3i4 4 2 2i5 4 2 2i3 3 2 1i1 2 1 1

Table 2 Sorting table of M-type nodesrsquo epidemic information dissemination capability in WeChat

Node Degree of centralitywithin the M-P network

Degree centrality withinthe M-M network

Important indicators of WeChatepidemic information dissemination capability

m4 6 3 3m5 2 0 2m1 4 3 1m2 4 3 1m3 4 3 1

Mathematical Problems in Engineering 9

epidemic in WeChat e Supernetwork model of WeChatepidemic information dissemination and the correspondingkey node identification method constructed in this study arethe initial attempts to research the information dissemi-nation of epidemic-related information in WeChat

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

PengWu and Di Zhao contributed to the design of the studyPeng Wu gave the main idea of the manuscript wrote thefirst draft and performed the design of figures All authorscontributed to the manuscript revision and read and ap-proved the submitted version

Acknowledgments

is work was supported by the National Social ScienceFund Project (18BGL238) China the China PostdoctoralScience Foundation Special Funding Project (2018T110724)China the Chinese Postdoctoral Science Fund GeneralSupport Project (2016M602236) China and the HenanPhilosophy and Social Science Planning Project(2017BJJ021) and Key Research Project of Teacher Educa-tion Curriculum Reform in Henan Province (2018-JSJYZD-008) China

References

[1] Science Net ldquoMining social network opinion leadersrdquo 2020httpblogsciencenetcnhomephpmodspaceampuid3075ampdoblogampid466991

[2] Surging News ldquoe 2019 WeChat annual data report is outrdquo2020 httpswwwthepapercnnewsDetail_forward_5480482

[3] L L Liu ldquoResearch on new coronary pneumonia epidemicreports from the perspective of the frameworkrdquo JournalismLover vol 5 pp 17ndash21 2020

[4] Z Deng X J Liu and Z D Kang ldquoResearch on the publicopinion propaganda and ideological education function ofuniversity new media in the prevention and control of majorepidemicsrdquo Studies in Ideological Education no 3 pp 38ndash432020

[5] Y S Chen ldquoResearch on spreading and governance of in-ternet rumors on public health emergencyrdquo E-Governmentno 6 pp 2ndash11 2020

[6] B J Wan C Guo Z Zhao et al ldquoCharacteristics and risksreflections of ldquoanti-epidemic fitness messagesrdquo delivered byWeChat during the COVID-19 epidemicrdquo Journal of XirsquoanPhysical Education University vol 37 no 3 pp 267ndash2752020

[7] Y Lu and L Zhang ldquoSocial media WeChat infers the de-velopment trend of COVID-19rdquo Journal of Infection no 81pp 82-83 2020

[8] A Nagurney and J Dong SupernetworksDecision-Making forthe Information Age Edward Elgar Publishing CheltenhamUK 2002

[9] Z P Wang and Z T Wang Supernetwork eory and itsApplication Science Press Beijing China 2008

[10] A Nagurney ldquoOptimal supply chain network design andredesign at minimal total cost and with demand satisfactionrdquoInternational Journal of Production Economics vol 128 no 1pp 200ndash208 2010

[11] A Nagurney M Yu and Q Qiang ldquoSupply chain networkdesign for critical needs with outsourcingrdquo Papers in RegionalScience vol 90 no 1 pp 123ndash142 2011

[12] L Zhu and J Cao ldquoSupernetwork optimization of emergencyresources allocation under disaster riskrdquo Chinese Journal ofManagement Science vol 20 no 6 pp 141ndash148 2012

[13] P Wu and H S Wang ldquoModeling of information dissemi-nation supernetwork in the emergencies and determination ofthe important nodes in the supernetworkrdquo Journal of theChina Society for Scientific and Technical Information vol 37no 7 pp 722ndash729 2012

[14] Y J Xi Y Z Dang and K J Liao ldquoKnowledge supernetworkmodel and its application in organizational knowledge sys-temsrdquo Journal of Management Sciences in China vol 12 no 3pp 12ndash21 2009

[15] P Wu H S Wang Y Li et al ldquoJudgment of importantcontrol nodes in the information dissemination super-net-work of emergencyrdquo Library and Information Service vol 57no 1 pp 112ndash116 2013

[16] Y Yu Research on Knowledge Supernetwork in OrganizationalKnowledge Management Dalian University of TechnologyDalian China 2009

[17] J L Segovia-juarez S Colombano and D KirschnerldquoIdentifying DNA splice sites using hypernetworks with ar-tificial molecular evolutionrdquo Biosystems vol 87 no 2-3pp 117ndash124 2007

[18] Z T Wang ldquoReflection on supernetworkrdquo Journal of Uni-versity of Shanghai for Science and Technology vol 33 no 3pp 229ndash237 2011

[19] J-B Liu J Cao A Alofi A AL-Mazrooei and A ElaiwldquoApplications of laplacian spectra for n-prism networksrdquoNeurocomputing vol 198 pp 69ndash73 2016

[20] J D Luo Lecture Notes on Social Network Analysis SocialSciences Academic Press Beijing China 2nd edition 2010

[21] S Hayat S Wang and J-B Liu ldquoValency-based topologicaldescriptors of chemical networks and their applicationsrdquoApplied Mathematical Modelling vol 60 pp 164ndash178 2018

10 Mathematical Problems in Engineering

are related where the value 1 is time-dependent and 0 is notrelevant us

WEIDSN f Gi Gp Gm1113872 1113873

Gi + Gp + Gm + Epminusi + Epminusm + Emminusi

I P M EIminusI EPminusP EMminusM Epminusi Epminusm Emminusi1113872 1113873

(1)

here Epminusi (pi ij) |ϕ(pi ij) 11113966 1113967 represents a set of as-sociation relationships between P and I nodes Epminusm

(pi1113864 ml) |φ(pi ml) 1 represents a collection of associ-ation relationships between P and M nodes and Emminusi

(ij1113966 ml) | c(ij ml) 1 represents a collection of associa-tions between I and M nodes

It can be seen that theWeChat Supernetworkmodel is anintegration of three epidemic information disseminationnetworks which reveals the complex composition andstructural form of epidemic information dissemination inWeChat

22 Construction of Adjacency Matrix and Network IntuitiveGraphofWeChatEpidemic InformationSupernetworkModelAt this stage we can use network analysis tools to measurevarious parameters of network analysis and network rela-tionship characterization software can draw network graphsfor intuitive comparison

Figure 1 is a schematic diagram of a three-networkintegration Supernetwork of a WeChat epidemic informa-tion dissemination system e figure is divided into threelayers e top layer is the WeChat group network enetwork members are WeChat groups ere may be as-sociations between the network members and the networkmembers may also be associated with the members of theother two layers mi represents the nodes in this layernetwork e middle layer of the network is the ordinaryWeChat user relationship network e network membersare ordinary WeChat users ere may be associations be-tween the network members and the network members mayalso be associated with members of the other two layers pi

represents nodes in this layer of the network e bottomlayer is the WeChat official account network e network

members are WeChat official accounts ere may be as-sociations between the network members and the networkmembers may also be associated with members of the othertwo layers of networks ii represents nodes in this layernetwork Figure 1 is a schematic diagram of a WeChatepidemic information dissemination Supernetwork inwhich ordinaryWeChat user p2 joinsWeChat groupm1 andordinary WeChat users p3 and p4 join WeChat groups m4and m5 After joining the WeChat groups m3 and m4 theordinary WeChat user p1 is added to the three WeChatgroups m2 m4 and m5 at the same time and the ordinaryWeChat user p5 is temporarily not added to any WeChatgroup WeChat groups m1 m2 and m5 are associated withthe public account network ordinary WeChat user p2 paysattention to the public accounts i2 and i3 ordinary user p3pays attention to the public accounts i1 i2 and i5 at the sametime and ordinary user p4 pays attention to the publicaccount i4 along with ordinary user p5 After paying at-tention to the public accounts i2 i4 and i5 the ordinaryWeChat user p1 does not follow anyWeChat public accountfor the time being Taking theWeChat epidemic informationdissemination Supernetwork as an example the boundary ofthe epidemic information dissemination subnetwork of theWeChat epidemic information dissemination system isdetermined and its many network nodes and their asso-ciations are established e rules for constructing the as-sociation relationship of network nodes are as follows If thetwo nodes in the schematic diagram of theWeChat epidemicinformation dissemination Supernetwork are connectedthey are marked as 1 otherwise they are marked as 0 Usingnetwork analysis software the adjacency matrix of theWeChat epidemic information dissemination Supernetworkcan be constructed as shown in Figure 2

At the same time the corresponding network analysisstandard file can be generated and imported into thespecified network relationship characterization softwarewhich can be processed according to specific needs orpurposes and used to then construct a network intuitive mapof the WeChat epidemic information disseminationSupernetwork as shown in Figure 3

e representative WeChat epidemic information dis-semination Supernetwork model outlined in this paper is a

m1

m2

m3m4 m5

p1p2

p3 p4

p5

i1

i2i3

i4

i5

Ordinary user relationship

network (including

WeChat friend circle)

WeChat group

network

WeChat public

account network

Figure 1 WeChat epidemic information dissemination Supernetwork

4 Mathematical Problems in Engineering

network of three different types of epidemic informationdissemination networks including the public account net-work WeChat group network and common WeChat userrelationship network e Supernetwork model containsthree relatively active and representative information carrierelements in the WeChat epidemic information dissemina-tion system such as WeChat public accounts WeChatgroups common WeChat users and their complex asso-ciations Compared with the epidemic information dis-semination network composed of similar nodes and theirassociations the Supernetwork model can better reflect thecomplex composition and structural form of the WeChatepidemic information dissemination network system so itcan be more accurate comprehensive and provide more in-depth WeChat epidemic information e communicationnetwork system conducts research and analysis lays afoundation and provides help for the management andguidance of subsequent WeChat epidemic informationdissemination

3 Identification of Key Nodes in WeChatEpidemic InformationDissemination Supernetwork

An important part of guiding the spread of epidemic-relatedinformation in WeChat is to first identify the key nodes inthe spread of WeChat epidemic information ese

important related nodes largely affect the spread of epi-demic-related information in WeChat

31 Traditional Key Node Identification Method e degreecentricity method in network analysis theory is the mainmethod for identifying key nodes in a network e formulais as follows

CD ni( 1113857 d ni( 1113857 1113944j

Xij 1113944j

Xji

CDprime ni( 1113857

d ni( 1113857

g minus 1

(2)

e value of Xji is 1 or 0 indicating whether node j isassociated with node i and g is the number of nodes in thenetwork In the network because the number of nodes ineach network is different and the number of large networknodes is large the standardization process must be dividedby the maximum possible number of relationships of a nodein the network that is g minus 1 relationships [19 20] Of coursein addition to the degree centrality method there are manymethods for identifying network central nodes but thedegree centrality method is relatively simple and straight-forward and the application scenarios of this method arealso broader with fewer restrictions on implementation [21]e network analysis tool was used to calculate the degreecentrality of all nodes in the Supernetwork as shown inFigure 3 and the system calculation results are as follows

00000000

0000

0000 0000 0000 0000 0000

00000000 00000000

00000000

0000

1000 00000000 0000 0000 0000 0000 0000 0000 000000000000 0000 0000 0000 0000 0000 0000 0000 0000 0000

0000 0000 0000 0000 0000 00000000 0000 00000000 0000 0000 0000 0000

0000000000000000 00000000

0000 0000000000000000

00000000

0000 0000 0000 000000000000 0000

000000000000 00000000

00000000

0000 0000 0000 00000000 0000 0000 0000

00000000

0000 0000 0000 00000000

00000000 0000 0000

0000 0000 0000 0000 0000 0000000000000000 0000 0000 0000

0000 0000 0000 00000000 0000

0000 0000 00000000 0000 0000 0000

0000 0000 0000 0000

0000 00000000

0000 0000 00000000 0000

0000 0000

1000 0000 0000 1000 0000 0000 000000001000

10001000

1000

1000

1000

10001000

10001000 1000 1000

1000 1000

1000

1000 0000 0000 0000 0000 00001000 0000 1000 1000 1000

1000

10001000 10001000

10001000

1000

10001000 1000 1000

1000

1000 10001000 1000 1000 1000

10001000 1000 1000

10001000 1000

1000 1000 10001000

100010001000 1000

10001000

1000 1000

1000 1000 10001000

1000 1000 10001000

1000

10001000

0000 0000123456789101112131415

m1m2m3m4m5

p3p4

p1p2

p5

i3i4i5

i2i1

1000

0000 1000 00000000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15m1 m2 m3 m4 m5 p1 p2 p3 p4 p5 i1 i2 i3 i4 i5

Figure 2 e adjacency matrix of the WeChat epidemic information Supernetwork

m1

m2

m3

m4

i1

i2

i3

i4

i5

p4

p5

p3

p1

m5

p2

Figure 3 Intuitive map of the WeChat epidemic information dissemination Supernetwork

Mathematical Problems in Engineering 5

From the results in the above figure we can see that thedegree of centrality of node p3 is 9 the degree of centrality ofp4 is 7 and the standardization of the two nodes is 064286and 05 respectively It can be seen that the p3 node and thep4 node are relatively important During the spread ofWeChat epidemic-related information monitoring andguiding these two nodes has a great impact on the overallinformation spread

32 Key Node Recognition Method Based on WeChatSupernetwork Degree centrality is currently one of the mostcommonly used key node identification methods but itsapplication in a Supernetwork has deficiencies e degreecentrality calculation here does not distinguish which subneteach node belongs to in the Supernetwork there is nodistinction between the relationships between nodes andthere is no difference between the relationships betweensubnets Accordingly this method cannot reflect the con-nection status of a node in the subnet to which it belongsnor can it reflect the propagation ability of the node in thesubnet to which it belongs similarly in the current situationthis method also fails to reflect the connection status of anode between subnetworks and it fails to measure thepropagation ability of the node between subnetworks Re-ferring to Figures 3 and 4 for example the i1 node has adegree of centrality of

CD(i1) d(i1) 1113944j

Xij 1113944j

Xji 3 (3)

And the m3 node has a degree of centrality of

CD(m3) d(m3) 1113944j

Xij 1113944j

Xji 4 (4)

According to the formula

CDprime ni( 1113857

d ni( 1113857

g minus 1 (5)

e standardized degree of centrality of i1 can be ob-tained as

CDprime (i1)

d(i1)

g minus 1 021429 (6)

And the standardized degree of centrality of node m3 is

CDprime (m3)

d(m3)

g minus 1 028571 (7)

us node i1 is not as important as m3 but in theprocess of epidemic information propagation in WeChat inthe Supernetwork i1 is associated with three unary subnetswhile m3 is only associated with the M-M network and P-Pnetwork and is not directly connected to the I-I networkFrom this perspective i1 is more important than m3 espread of epidemic information in WeChat has uniquefeatures For example the ability of ordinary WeChat usersto spread information in the circle of friends is related to thenumber of their friends the ability of the public account tospread information in WeChat is related to the number of

fans and the ability to spread information inWeChat groupsand the number of WeChat group members is related enodes with strong propagation ability are more importantand the identificationmethods of these key nodes inWeChatneed to be rebuilt

In order to avoid the above deficiencies this paperproposes a new comprehensive method for identifying keynodes in WeChat epidemic information disseminationbased on a Supernetwork part of which is based on animprovement of the decision method proposed previously[13] and the other part is mainly constructed based on thecharacteristics of the spread of epidemic information inWeChat e new method is briefly described as follows

Let ni be any node in the Supernetwork QCD(ni)

represents the degree of centrality of ni in the entireSupernetwork and ZCD(ni) is the degree of centrality of ni

in the unary subnet to which it belongs

(1) Step 1 Calculate and compare the degree of cen-trality of each node in the entire Supernetwork

(2) Step 2 Calculate and compare the degree centralityof all nodes in the M-P binary subnetwork and theI-P binary subnetwork in the M-P binary subnet-work and I-P binary subnetwork to which theybelong

(3) Step 3 Calculate and compare the degree centralityof all the individuals in the entire Supernetworksystem in the subunit networks to which they belong

(4) Step 4 Calculate and compare the internetworkpropagation capabilities of each node in the subnet ofa unitary network in the Supernetwork Let LZS(ni)

be the number of unitary subnetworks connected bynode ni and ZJBS(ni) the edges of node ni betweenthe unitary subnetworks e number can be ob-tained from the above analysisZJBS(ni) QCD(ni) minus ZCD(ni) the network prop-agation ability of the node ni in the Supernetwork isexpressed by ZJCN(ni) and the calculation andcomparison methods are as follows

Select Case LZS(A)

Case ISgt LZS(B)

ZJCN(A)gtZJCN(B)

Case ISlt LZS(B)

ZJCN(A)ltZJCN(B)

Case IS LZS(B)

Select Case ZJBS(A)

Case ISgtZJBS(B)

ZJCN(A)gtZJCN(B)

Case ISltZJBS(B)

ZJCN(A)ltZJCN(B)

Case IS ZJBS(B)

ZJCN(A) ZJCN(B)

End SelectEnd Select

6 Mathematical Problems in Engineering

(5) Step 5 Calculate and compare the internetworkpropagation capability ZJCNJ(ni) between theM-type nodes in the M-P binary subnetwork and theI-type nodes in the I-P binary subnetwork under thecorresponding binary subnetwork view LetJMminusPCD(ni) represent the degree of centrality of ni inthe M-P binary subnetwork to which it belongs andlet JIminusPCD(ni) represent the degree of centrality of ni

in the I-P binary subnetwork to which it belongs andthe calculation method of ZJCNJ(ni) is as followsSelect Case ni

Case IS isinM

ZJCNJ(ni) JMminusPCD(ni) minus ZCD(ni)

Case IS isin I

ZJCNJ(ni) JIminusPCD(ni) minus ZCD(ni)

End Select(6) Combining the results of the above steps key nodes

are identified

In the above steps Step 2 prepares for the calculation andcomparison of the number of fans of the public account andthe number of members in the WeChat group is determinedin Step 5 Step 3 the calculation result can also obtain thenumber of friends of ordinary WeChat users in the circle offriends e circle of friends is one of the main channels forordinary users to disseminate information in WeChat enumber of friends in the circle of friends is an importantcriterion for identifying the ability of ordinaryWeChat usersto disseminate information Step 4 compares the unarysubnet internetwork propagation capabilities of each node inthe Supernetwork view by the number of unary subnetworksconnected by the nodes and the number of nodes connectedbetween the unary subnetworks A ranking table was createdshowing the strengths and weaknesses of the unary subnetrsquosinternetwork spreading ability under the Supernetworkvision Among them QCD(ni) can be obtained by Step 1ZCD(ni) can be obtained by Step 3 and the individualrsquosZJBS(ni) can be obtained by the difference between QCD(ni)

and ZCD(ni) of an individual Firstly it is judged based onthe number of unary subnetworks connected to the node

e number of unary subnetworks connected to node A isgreater than the number of unary subnetworks connected tonode B which indicates that the internetwork communi-cation capability of node A is stronger than that of node B Ifthe number of unary subnetworks connected to node A isless than the number of unary subnetworks connected tonode B it indicates that the internetwork propagation ca-pability of node A between unary subnetworks is weakerthan that of node B If the number of unary subnetworksconnected to node A is the same as the number of unarysubnetworks connected to node B further judgments needto be made based on the number of edges between the unarysubnetworks of nodes Step 5 is mainly based on the cal-culation results of Step 2 and Step 3 and calculates andcompares the number of fans of the public account and thenumber of members of the WeChat group in the WeChatSupernetwork e information dissemination ability ofnodes is measured to provide a reference for the identifi-cation of key nodes is step calculates the internetworkpropagation capability between theM-type nodes in theM-Pbinary subnetwork and the I-type nodes in the I-P binarysubnetwork from the binary subnetwork perspective

Taking the example shown in Figure 3 for verificationand analysis

(1) Step 1 e calculation result is shown in Figure 4(2) Step 2 e screenshots of the system calculation

results are shown in Figures 5 and 6(3) Step 3 e result is shown in Figure 7(4) Step 4 e results are shown in Table 1(5) Combining the comparison and calculation results

of Step 2 and Figures 5 and 6 with the comparisonand calculation results of Step 3 and Figure 7 thecalculation and comparison results of this step areshown in Tables 2 and 3

(6) From the perspective of intranetwork propagationFigure 7 shows that the degree of centrality of i3 i4and i5 in the I-I network is the same and the highestand the propagation ability of i3 i4 and i5 in thenetwork is also the strongest Nodesm1m2m3 and

8 9000 64286 01229 7000 50000 00954 6000

50005000

500050005000500040004000300030003000

42857 008110 35714

35714

35714357143571435714

12 i2671215 0068

006800680068

00685000 35714 0068

0068

3 2857128571 0054

00541413

2142921429

21429115 0041

00410041

Degree1

NrmDegree2

Share3

p3p4m4p5

p1p2m1m2

i3i4

i5

i1m5

m3

Figure 4 e degree of centrality of all nodes in the WeChat epidemic information Supernetwork

Mathematical Problems in Engineering 7

m4 have strong propagation capabilities in the M-Mnetwork In the P-P network p3 and p4 are thestrongest nodes in the network From the perspectiveof internetwork propagation Table 1 shows that thenumber of subnetworks connected by nodes p3 andi2 is larger and the number of interconnected edgesbetween networks is also larger so their internet-work propagation capabilities are stronger edegree centrality value of such nodes may not be

large but its influence on the propagation effect isoften large which is worthy of attention It can alsobe seen from Table 1 that although m3 has thestrongest propagation capability in the M-M net-work and i1 has the weakest propagation capabilityin the I-I network in Figure 7 from the perspective ofinternetwork propagation i1 connects three subnetsthere are 2 internetwork edges m3 only connects 2subnets and there is only 1 internetwork edge so i1

3 7000 77778 01754 5000

50004000400040004000300020002000

55556 01255 55556 01252 44444

444444444444444333332222222222

01007 010010 01009 01008 00751 00506 0050

Degree1

NrmDegree2

Share3

p3p4p5p2i2i5i4i3p1i1

Figure 5 e degree of centrality of all nodes in the I-P network

6000600060005000400040004000300020002000

666676666766667

014301430143

55556 0119444444444444444

009500950095

33333 007122222 0048

8 p34 m49 p46 p12 m21 m13 m37 p25 m510 p5 22222 0048

Degree1

NrmDegree2

Share3

Figure 6 e degree of centrality of all nodes in the M-P network

12345

34125

34521

m1m2m3m4m5

Degree1

30003000300030000000

NrmDegree2

0000

750007500075000

75000

Share3

0000

0250025002500250

p3p4p1p2p5

Degree1

40004000200020002000

2000

20002000

NrmDegree2

100000100000500005000050000

500005000050000

Share3

Degree1

NrmDegree2

Share3

02860286014301430143

10001000 25000

25000

02500250025001250125

i3i4i5i2i1

Figure 7 e degree of centrality of each node in the unary subnet to which it belongs

8 Mathematical Problems in Engineering

is slightly better than m3 in terms of internetworkcommunication capability From the perspective ofthe spread of epidemic-related information inWeChat Figure 7 shows that p3 and p4 have a strongability to spread epidemic-related information in theWeChat circle of friends Under the same conditionsthe spread of epidemic-related information of thesetwo ordinary user nodes is faster e spreadingrange is wide Table 2 shows that m4 has a strongspreading capability in WeChat group nodes Underthe same conditions the information spreadingspeed of this WeChat group node is faster and thespreading range is wider Table 3 shows i2 in thepublic account category e dissemination capa-bility of the node is strong Under the same con-ditions the public information nodersquos epidemic-related information spreads faster more widely Toguide the dissemination of epidemic-related infor-mation in WeChat it is best to guide the

abovementioned WeChat nodes with a strong abilityto disseminate epidemic-related information

e new method also identifies the importance of or-dinary WeChat users WeChat groups and official accountsfrom the perspective of information diffusion based on theparticularity of the spread of WeChat epidemic-relatedinformation in order to be more comprehensive andreasonable

4 Conclusions

is article mainly concerns the model construction and keynode identification of the WeChat epidemic-related infor-mation dissemination Supernetwork e identificationmethod can be roughly divided into two parts One part isbased on the improvement of the decision method proposedpreviously [13] and the other part of it is mainly based onthe characteristics of the spread of information related to the

Table 1 Sequence table of nodersquos internetwork epidemic information dissemination ability

Node Number of unary subnets associated Number of relationshipsp3 3 5i2 3 4p2 3 3p4 3 3i5 3 3m1 3 2i1 3 2m2 3 2m5 2 3p1 2 3m4 2 3p5 2 3i4 2 2m3 2 1i3 2 1

Table 3 Sorting table of the spreading capacity of epidemic information in WeChat for Class I nodes

Node Degree of centralitywithin the I-P network

Degree of centrality withinthe I-I network

Important indicators of WeChatepidemic information dissemination capability

i2 4 1 3i4 4 2 2i5 4 2 2i3 3 2 1i1 2 1 1

Table 2 Sorting table of M-type nodesrsquo epidemic information dissemination capability in WeChat

Node Degree of centralitywithin the M-P network

Degree centrality withinthe M-M network

Important indicators of WeChatepidemic information dissemination capability

m4 6 3 3m5 2 0 2m1 4 3 1m2 4 3 1m3 4 3 1

Mathematical Problems in Engineering 9

epidemic in WeChat e Supernetwork model of WeChatepidemic information dissemination and the correspondingkey node identification method constructed in this study arethe initial attempts to research the information dissemi-nation of epidemic-related information in WeChat

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

PengWu and Di Zhao contributed to the design of the studyPeng Wu gave the main idea of the manuscript wrote thefirst draft and performed the design of figures All authorscontributed to the manuscript revision and read and ap-proved the submitted version

Acknowledgments

is work was supported by the National Social ScienceFund Project (18BGL238) China the China PostdoctoralScience Foundation Special Funding Project (2018T110724)China the Chinese Postdoctoral Science Fund GeneralSupport Project (2016M602236) China and the HenanPhilosophy and Social Science Planning Project(2017BJJ021) and Key Research Project of Teacher Educa-tion Curriculum Reform in Henan Province (2018-JSJYZD-008) China

References

[1] Science Net ldquoMining social network opinion leadersrdquo 2020httpblogsciencenetcnhomephpmodspaceampuid3075ampdoblogampid466991

[2] Surging News ldquoe 2019 WeChat annual data report is outrdquo2020 httpswwwthepapercnnewsDetail_forward_5480482

[3] L L Liu ldquoResearch on new coronary pneumonia epidemicreports from the perspective of the frameworkrdquo JournalismLover vol 5 pp 17ndash21 2020

[4] Z Deng X J Liu and Z D Kang ldquoResearch on the publicopinion propaganda and ideological education function ofuniversity new media in the prevention and control of majorepidemicsrdquo Studies in Ideological Education no 3 pp 38ndash432020

[5] Y S Chen ldquoResearch on spreading and governance of in-ternet rumors on public health emergencyrdquo E-Governmentno 6 pp 2ndash11 2020

[6] B J Wan C Guo Z Zhao et al ldquoCharacteristics and risksreflections of ldquoanti-epidemic fitness messagesrdquo delivered byWeChat during the COVID-19 epidemicrdquo Journal of XirsquoanPhysical Education University vol 37 no 3 pp 267ndash2752020

[7] Y Lu and L Zhang ldquoSocial media WeChat infers the de-velopment trend of COVID-19rdquo Journal of Infection no 81pp 82-83 2020

[8] A Nagurney and J Dong SupernetworksDecision-Making forthe Information Age Edward Elgar Publishing CheltenhamUK 2002

[9] Z P Wang and Z T Wang Supernetwork eory and itsApplication Science Press Beijing China 2008

[10] A Nagurney ldquoOptimal supply chain network design andredesign at minimal total cost and with demand satisfactionrdquoInternational Journal of Production Economics vol 128 no 1pp 200ndash208 2010

[11] A Nagurney M Yu and Q Qiang ldquoSupply chain networkdesign for critical needs with outsourcingrdquo Papers in RegionalScience vol 90 no 1 pp 123ndash142 2011

[12] L Zhu and J Cao ldquoSupernetwork optimization of emergencyresources allocation under disaster riskrdquo Chinese Journal ofManagement Science vol 20 no 6 pp 141ndash148 2012

[13] P Wu and H S Wang ldquoModeling of information dissemi-nation supernetwork in the emergencies and determination ofthe important nodes in the supernetworkrdquo Journal of theChina Society for Scientific and Technical Information vol 37no 7 pp 722ndash729 2012

[14] Y J Xi Y Z Dang and K J Liao ldquoKnowledge supernetworkmodel and its application in organizational knowledge sys-temsrdquo Journal of Management Sciences in China vol 12 no 3pp 12ndash21 2009

[15] P Wu H S Wang Y Li et al ldquoJudgment of importantcontrol nodes in the information dissemination super-net-work of emergencyrdquo Library and Information Service vol 57no 1 pp 112ndash116 2013

[16] Y Yu Research on Knowledge Supernetwork in OrganizationalKnowledge Management Dalian University of TechnologyDalian China 2009

[17] J L Segovia-juarez S Colombano and D KirschnerldquoIdentifying DNA splice sites using hypernetworks with ar-tificial molecular evolutionrdquo Biosystems vol 87 no 2-3pp 117ndash124 2007

[18] Z T Wang ldquoReflection on supernetworkrdquo Journal of Uni-versity of Shanghai for Science and Technology vol 33 no 3pp 229ndash237 2011

[19] J-B Liu J Cao A Alofi A AL-Mazrooei and A ElaiwldquoApplications of laplacian spectra for n-prism networksrdquoNeurocomputing vol 198 pp 69ndash73 2016

[20] J D Luo Lecture Notes on Social Network Analysis SocialSciences Academic Press Beijing China 2nd edition 2010

[21] S Hayat S Wang and J-B Liu ldquoValency-based topologicaldescriptors of chemical networks and their applicationsrdquoApplied Mathematical Modelling vol 60 pp 164ndash178 2018

10 Mathematical Problems in Engineering

network of three different types of epidemic informationdissemination networks including the public account net-work WeChat group network and common WeChat userrelationship network e Supernetwork model containsthree relatively active and representative information carrierelements in the WeChat epidemic information dissemina-tion system such as WeChat public accounts WeChatgroups common WeChat users and their complex asso-ciations Compared with the epidemic information dis-semination network composed of similar nodes and theirassociations the Supernetwork model can better reflect thecomplex composition and structural form of the WeChatepidemic information dissemination network system so itcan be more accurate comprehensive and provide more in-depth WeChat epidemic information e communicationnetwork system conducts research and analysis lays afoundation and provides help for the management andguidance of subsequent WeChat epidemic informationdissemination

3 Identification of Key Nodes in WeChatEpidemic InformationDissemination Supernetwork

An important part of guiding the spread of epidemic-relatedinformation in WeChat is to first identify the key nodes inthe spread of WeChat epidemic information ese

important related nodes largely affect the spread of epi-demic-related information in WeChat

31 Traditional Key Node Identification Method e degreecentricity method in network analysis theory is the mainmethod for identifying key nodes in a network e formulais as follows

CD ni( 1113857 d ni( 1113857 1113944j

Xij 1113944j

Xji

CDprime ni( 1113857

d ni( 1113857

g minus 1

(2)

e value of Xji is 1 or 0 indicating whether node j isassociated with node i and g is the number of nodes in thenetwork In the network because the number of nodes ineach network is different and the number of large networknodes is large the standardization process must be dividedby the maximum possible number of relationships of a nodein the network that is g minus 1 relationships [19 20] Of coursein addition to the degree centrality method there are manymethods for identifying network central nodes but thedegree centrality method is relatively simple and straight-forward and the application scenarios of this method arealso broader with fewer restrictions on implementation [21]e network analysis tool was used to calculate the degreecentrality of all nodes in the Supernetwork as shown inFigure 3 and the system calculation results are as follows

00000000

0000

0000 0000 0000 0000 0000

00000000 00000000

00000000

0000

1000 00000000 0000 0000 0000 0000 0000 0000 000000000000 0000 0000 0000 0000 0000 0000 0000 0000 0000

0000 0000 0000 0000 0000 00000000 0000 00000000 0000 0000 0000 0000

0000000000000000 00000000

0000 0000000000000000

00000000

0000 0000 0000 000000000000 0000

000000000000 00000000

00000000

0000 0000 0000 00000000 0000 0000 0000

00000000

0000 0000 0000 00000000

00000000 0000 0000

0000 0000 0000 0000 0000 0000000000000000 0000 0000 0000

0000 0000 0000 00000000 0000

0000 0000 00000000 0000 0000 0000

0000 0000 0000 0000

0000 00000000

0000 0000 00000000 0000

0000 0000

1000 0000 0000 1000 0000 0000 000000001000

10001000

1000

1000

1000

10001000

10001000 1000 1000

1000 1000

1000

1000 0000 0000 0000 0000 00001000 0000 1000 1000 1000

1000

10001000 10001000

10001000

1000

10001000 1000 1000

1000

1000 10001000 1000 1000 1000

10001000 1000 1000

10001000 1000

1000 1000 10001000

100010001000 1000

10001000

1000 1000

1000 1000 10001000

1000 1000 10001000

1000

10001000

0000 0000123456789101112131415

m1m2m3m4m5

p3p4

p1p2

p5

i3i4i5

i2i1

1000

0000 1000 00000000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15m1 m2 m3 m4 m5 p1 p2 p3 p4 p5 i1 i2 i3 i4 i5

Figure 2 e adjacency matrix of the WeChat epidemic information Supernetwork

m1

m2

m3

m4

i1

i2

i3

i4

i5

p4

p5

p3

p1

m5

p2

Figure 3 Intuitive map of the WeChat epidemic information dissemination Supernetwork

Mathematical Problems in Engineering 5

From the results in the above figure we can see that thedegree of centrality of node p3 is 9 the degree of centrality ofp4 is 7 and the standardization of the two nodes is 064286and 05 respectively It can be seen that the p3 node and thep4 node are relatively important During the spread ofWeChat epidemic-related information monitoring andguiding these two nodes has a great impact on the overallinformation spread

32 Key Node Recognition Method Based on WeChatSupernetwork Degree centrality is currently one of the mostcommonly used key node identification methods but itsapplication in a Supernetwork has deficiencies e degreecentrality calculation here does not distinguish which subneteach node belongs to in the Supernetwork there is nodistinction between the relationships between nodes andthere is no difference between the relationships betweensubnets Accordingly this method cannot reflect the con-nection status of a node in the subnet to which it belongsnor can it reflect the propagation ability of the node in thesubnet to which it belongs similarly in the current situationthis method also fails to reflect the connection status of anode between subnetworks and it fails to measure thepropagation ability of the node between subnetworks Re-ferring to Figures 3 and 4 for example the i1 node has adegree of centrality of

CD(i1) d(i1) 1113944j

Xij 1113944j

Xji 3 (3)

And the m3 node has a degree of centrality of

CD(m3) d(m3) 1113944j

Xij 1113944j

Xji 4 (4)

According to the formula

CDprime ni( 1113857

d ni( 1113857

g minus 1 (5)

e standardized degree of centrality of i1 can be ob-tained as

CDprime (i1)

d(i1)

g minus 1 021429 (6)

And the standardized degree of centrality of node m3 is

CDprime (m3)

d(m3)

g minus 1 028571 (7)

us node i1 is not as important as m3 but in theprocess of epidemic information propagation in WeChat inthe Supernetwork i1 is associated with three unary subnetswhile m3 is only associated with the M-M network and P-Pnetwork and is not directly connected to the I-I networkFrom this perspective i1 is more important than m3 espread of epidemic information in WeChat has uniquefeatures For example the ability of ordinary WeChat usersto spread information in the circle of friends is related to thenumber of their friends the ability of the public account tospread information in WeChat is related to the number of

fans and the ability to spread information inWeChat groupsand the number of WeChat group members is related enodes with strong propagation ability are more importantand the identificationmethods of these key nodes inWeChatneed to be rebuilt

In order to avoid the above deficiencies this paperproposes a new comprehensive method for identifying keynodes in WeChat epidemic information disseminationbased on a Supernetwork part of which is based on animprovement of the decision method proposed previously[13] and the other part is mainly constructed based on thecharacteristics of the spread of epidemic information inWeChat e new method is briefly described as follows

Let ni be any node in the Supernetwork QCD(ni)

represents the degree of centrality of ni in the entireSupernetwork and ZCD(ni) is the degree of centrality of ni

in the unary subnet to which it belongs

(1) Step 1 Calculate and compare the degree of cen-trality of each node in the entire Supernetwork

(2) Step 2 Calculate and compare the degree centralityof all nodes in the M-P binary subnetwork and theI-P binary subnetwork in the M-P binary subnet-work and I-P binary subnetwork to which theybelong

(3) Step 3 Calculate and compare the degree centralityof all the individuals in the entire Supernetworksystem in the subunit networks to which they belong

(4) Step 4 Calculate and compare the internetworkpropagation capabilities of each node in the subnet ofa unitary network in the Supernetwork Let LZS(ni)

be the number of unitary subnetworks connected bynode ni and ZJBS(ni) the edges of node ni betweenthe unitary subnetworks e number can be ob-tained from the above analysisZJBS(ni) QCD(ni) minus ZCD(ni) the network prop-agation ability of the node ni in the Supernetwork isexpressed by ZJCN(ni) and the calculation andcomparison methods are as follows

Select Case LZS(A)

Case ISgt LZS(B)

ZJCN(A)gtZJCN(B)

Case ISlt LZS(B)

ZJCN(A)ltZJCN(B)

Case IS LZS(B)

Select Case ZJBS(A)

Case ISgtZJBS(B)

ZJCN(A)gtZJCN(B)

Case ISltZJBS(B)

ZJCN(A)ltZJCN(B)

Case IS ZJBS(B)

ZJCN(A) ZJCN(B)

End SelectEnd Select

6 Mathematical Problems in Engineering

(5) Step 5 Calculate and compare the internetworkpropagation capability ZJCNJ(ni) between theM-type nodes in the M-P binary subnetwork and theI-type nodes in the I-P binary subnetwork under thecorresponding binary subnetwork view LetJMminusPCD(ni) represent the degree of centrality of ni inthe M-P binary subnetwork to which it belongs andlet JIminusPCD(ni) represent the degree of centrality of ni

in the I-P binary subnetwork to which it belongs andthe calculation method of ZJCNJ(ni) is as followsSelect Case ni

Case IS isinM

ZJCNJ(ni) JMminusPCD(ni) minus ZCD(ni)

Case IS isin I

ZJCNJ(ni) JIminusPCD(ni) minus ZCD(ni)

End Select(6) Combining the results of the above steps key nodes

are identified

In the above steps Step 2 prepares for the calculation andcomparison of the number of fans of the public account andthe number of members in the WeChat group is determinedin Step 5 Step 3 the calculation result can also obtain thenumber of friends of ordinary WeChat users in the circle offriends e circle of friends is one of the main channels forordinary users to disseminate information in WeChat enumber of friends in the circle of friends is an importantcriterion for identifying the ability of ordinaryWeChat usersto disseminate information Step 4 compares the unarysubnet internetwork propagation capabilities of each node inthe Supernetwork view by the number of unary subnetworksconnected by the nodes and the number of nodes connectedbetween the unary subnetworks A ranking table was createdshowing the strengths and weaknesses of the unary subnetrsquosinternetwork spreading ability under the Supernetworkvision Among them QCD(ni) can be obtained by Step 1ZCD(ni) can be obtained by Step 3 and the individualrsquosZJBS(ni) can be obtained by the difference between QCD(ni)

and ZCD(ni) of an individual Firstly it is judged based onthe number of unary subnetworks connected to the node

e number of unary subnetworks connected to node A isgreater than the number of unary subnetworks connected tonode B which indicates that the internetwork communi-cation capability of node A is stronger than that of node B Ifthe number of unary subnetworks connected to node A isless than the number of unary subnetworks connected tonode B it indicates that the internetwork propagation ca-pability of node A between unary subnetworks is weakerthan that of node B If the number of unary subnetworksconnected to node A is the same as the number of unarysubnetworks connected to node B further judgments needto be made based on the number of edges between the unarysubnetworks of nodes Step 5 is mainly based on the cal-culation results of Step 2 and Step 3 and calculates andcompares the number of fans of the public account and thenumber of members of the WeChat group in the WeChatSupernetwork e information dissemination ability ofnodes is measured to provide a reference for the identifi-cation of key nodes is step calculates the internetworkpropagation capability between theM-type nodes in theM-Pbinary subnetwork and the I-type nodes in the I-P binarysubnetwork from the binary subnetwork perspective

Taking the example shown in Figure 3 for verificationand analysis

(1) Step 1 e calculation result is shown in Figure 4(2) Step 2 e screenshots of the system calculation

results are shown in Figures 5 and 6(3) Step 3 e result is shown in Figure 7(4) Step 4 e results are shown in Table 1(5) Combining the comparison and calculation results

of Step 2 and Figures 5 and 6 with the comparisonand calculation results of Step 3 and Figure 7 thecalculation and comparison results of this step areshown in Tables 2 and 3

(6) From the perspective of intranetwork propagationFigure 7 shows that the degree of centrality of i3 i4and i5 in the I-I network is the same and the highestand the propagation ability of i3 i4 and i5 in thenetwork is also the strongest Nodesm1m2m3 and

8 9000 64286 01229 7000 50000 00954 6000

50005000

500050005000500040004000300030003000

42857 008110 35714

35714

35714357143571435714

12 i2671215 0068

006800680068

00685000 35714 0068

0068

3 2857128571 0054

00541413

2142921429

21429115 0041

00410041

Degree1

NrmDegree2

Share3

p3p4m4p5

p1p2m1m2

i3i4

i5

i1m5

m3

Figure 4 e degree of centrality of all nodes in the WeChat epidemic information Supernetwork

Mathematical Problems in Engineering 7

m4 have strong propagation capabilities in the M-Mnetwork In the P-P network p3 and p4 are thestrongest nodes in the network From the perspectiveof internetwork propagation Table 1 shows that thenumber of subnetworks connected by nodes p3 andi2 is larger and the number of interconnected edgesbetween networks is also larger so their internet-work propagation capabilities are stronger edegree centrality value of such nodes may not be

large but its influence on the propagation effect isoften large which is worthy of attention It can alsobe seen from Table 1 that although m3 has thestrongest propagation capability in the M-M net-work and i1 has the weakest propagation capabilityin the I-I network in Figure 7 from the perspective ofinternetwork propagation i1 connects three subnetsthere are 2 internetwork edges m3 only connects 2subnets and there is only 1 internetwork edge so i1

3 7000 77778 01754 5000

50004000400040004000300020002000

55556 01255 55556 01252 44444

444444444444444333332222222222

01007 010010 01009 01008 00751 00506 0050

Degree1

NrmDegree2

Share3

p3p4p5p2i2i5i4i3p1i1

Figure 5 e degree of centrality of all nodes in the I-P network

6000600060005000400040004000300020002000

666676666766667

014301430143

55556 0119444444444444444

009500950095

33333 007122222 0048

8 p34 m49 p46 p12 m21 m13 m37 p25 m510 p5 22222 0048

Degree1

NrmDegree2

Share3

Figure 6 e degree of centrality of all nodes in the M-P network

12345

34125

34521

m1m2m3m4m5

Degree1

30003000300030000000

NrmDegree2

0000

750007500075000

75000

Share3

0000

0250025002500250

p3p4p1p2p5

Degree1

40004000200020002000

2000

20002000

NrmDegree2

100000100000500005000050000

500005000050000

Share3

Degree1

NrmDegree2

Share3

02860286014301430143

10001000 25000

25000

02500250025001250125

i3i4i5i2i1

Figure 7 e degree of centrality of each node in the unary subnet to which it belongs

8 Mathematical Problems in Engineering

is slightly better than m3 in terms of internetworkcommunication capability From the perspective ofthe spread of epidemic-related information inWeChat Figure 7 shows that p3 and p4 have a strongability to spread epidemic-related information in theWeChat circle of friends Under the same conditionsthe spread of epidemic-related information of thesetwo ordinary user nodes is faster e spreadingrange is wide Table 2 shows that m4 has a strongspreading capability in WeChat group nodes Underthe same conditions the information spreadingspeed of this WeChat group node is faster and thespreading range is wider Table 3 shows i2 in thepublic account category e dissemination capa-bility of the node is strong Under the same con-ditions the public information nodersquos epidemic-related information spreads faster more widely Toguide the dissemination of epidemic-related infor-mation in WeChat it is best to guide the

abovementioned WeChat nodes with a strong abilityto disseminate epidemic-related information

e new method also identifies the importance of or-dinary WeChat users WeChat groups and official accountsfrom the perspective of information diffusion based on theparticularity of the spread of WeChat epidemic-relatedinformation in order to be more comprehensive andreasonable

4 Conclusions

is article mainly concerns the model construction and keynode identification of the WeChat epidemic-related infor-mation dissemination Supernetwork e identificationmethod can be roughly divided into two parts One part isbased on the improvement of the decision method proposedpreviously [13] and the other part of it is mainly based onthe characteristics of the spread of information related to the

Table 1 Sequence table of nodersquos internetwork epidemic information dissemination ability

Node Number of unary subnets associated Number of relationshipsp3 3 5i2 3 4p2 3 3p4 3 3i5 3 3m1 3 2i1 3 2m2 3 2m5 2 3p1 2 3m4 2 3p5 2 3i4 2 2m3 2 1i3 2 1

Table 3 Sorting table of the spreading capacity of epidemic information in WeChat for Class I nodes

Node Degree of centralitywithin the I-P network

Degree of centrality withinthe I-I network

Important indicators of WeChatepidemic information dissemination capability

i2 4 1 3i4 4 2 2i5 4 2 2i3 3 2 1i1 2 1 1

Table 2 Sorting table of M-type nodesrsquo epidemic information dissemination capability in WeChat

Node Degree of centralitywithin the M-P network

Degree centrality withinthe M-M network

Important indicators of WeChatepidemic information dissemination capability

m4 6 3 3m5 2 0 2m1 4 3 1m2 4 3 1m3 4 3 1

Mathematical Problems in Engineering 9

epidemic in WeChat e Supernetwork model of WeChatepidemic information dissemination and the correspondingkey node identification method constructed in this study arethe initial attempts to research the information dissemi-nation of epidemic-related information in WeChat

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

PengWu and Di Zhao contributed to the design of the studyPeng Wu gave the main idea of the manuscript wrote thefirst draft and performed the design of figures All authorscontributed to the manuscript revision and read and ap-proved the submitted version

Acknowledgments

is work was supported by the National Social ScienceFund Project (18BGL238) China the China PostdoctoralScience Foundation Special Funding Project (2018T110724)China the Chinese Postdoctoral Science Fund GeneralSupport Project (2016M602236) China and the HenanPhilosophy and Social Science Planning Project(2017BJJ021) and Key Research Project of Teacher Educa-tion Curriculum Reform in Henan Province (2018-JSJYZD-008) China

References

[1] Science Net ldquoMining social network opinion leadersrdquo 2020httpblogsciencenetcnhomephpmodspaceampuid3075ampdoblogampid466991

[2] Surging News ldquoe 2019 WeChat annual data report is outrdquo2020 httpswwwthepapercnnewsDetail_forward_5480482

[3] L L Liu ldquoResearch on new coronary pneumonia epidemicreports from the perspective of the frameworkrdquo JournalismLover vol 5 pp 17ndash21 2020

[4] Z Deng X J Liu and Z D Kang ldquoResearch on the publicopinion propaganda and ideological education function ofuniversity new media in the prevention and control of majorepidemicsrdquo Studies in Ideological Education no 3 pp 38ndash432020

[5] Y S Chen ldquoResearch on spreading and governance of in-ternet rumors on public health emergencyrdquo E-Governmentno 6 pp 2ndash11 2020

[6] B J Wan C Guo Z Zhao et al ldquoCharacteristics and risksreflections of ldquoanti-epidemic fitness messagesrdquo delivered byWeChat during the COVID-19 epidemicrdquo Journal of XirsquoanPhysical Education University vol 37 no 3 pp 267ndash2752020

[7] Y Lu and L Zhang ldquoSocial media WeChat infers the de-velopment trend of COVID-19rdquo Journal of Infection no 81pp 82-83 2020

[8] A Nagurney and J Dong SupernetworksDecision-Making forthe Information Age Edward Elgar Publishing CheltenhamUK 2002

[9] Z P Wang and Z T Wang Supernetwork eory and itsApplication Science Press Beijing China 2008

[10] A Nagurney ldquoOptimal supply chain network design andredesign at minimal total cost and with demand satisfactionrdquoInternational Journal of Production Economics vol 128 no 1pp 200ndash208 2010

[11] A Nagurney M Yu and Q Qiang ldquoSupply chain networkdesign for critical needs with outsourcingrdquo Papers in RegionalScience vol 90 no 1 pp 123ndash142 2011

[12] L Zhu and J Cao ldquoSupernetwork optimization of emergencyresources allocation under disaster riskrdquo Chinese Journal ofManagement Science vol 20 no 6 pp 141ndash148 2012

[13] P Wu and H S Wang ldquoModeling of information dissemi-nation supernetwork in the emergencies and determination ofthe important nodes in the supernetworkrdquo Journal of theChina Society for Scientific and Technical Information vol 37no 7 pp 722ndash729 2012

[14] Y J Xi Y Z Dang and K J Liao ldquoKnowledge supernetworkmodel and its application in organizational knowledge sys-temsrdquo Journal of Management Sciences in China vol 12 no 3pp 12ndash21 2009

[15] P Wu H S Wang Y Li et al ldquoJudgment of importantcontrol nodes in the information dissemination super-net-work of emergencyrdquo Library and Information Service vol 57no 1 pp 112ndash116 2013

[16] Y Yu Research on Knowledge Supernetwork in OrganizationalKnowledge Management Dalian University of TechnologyDalian China 2009

[17] J L Segovia-juarez S Colombano and D KirschnerldquoIdentifying DNA splice sites using hypernetworks with ar-tificial molecular evolutionrdquo Biosystems vol 87 no 2-3pp 117ndash124 2007

[18] Z T Wang ldquoReflection on supernetworkrdquo Journal of Uni-versity of Shanghai for Science and Technology vol 33 no 3pp 229ndash237 2011

[19] J-B Liu J Cao A Alofi A AL-Mazrooei and A ElaiwldquoApplications of laplacian spectra for n-prism networksrdquoNeurocomputing vol 198 pp 69ndash73 2016

[20] J D Luo Lecture Notes on Social Network Analysis SocialSciences Academic Press Beijing China 2nd edition 2010

[21] S Hayat S Wang and J-B Liu ldquoValency-based topologicaldescriptors of chemical networks and their applicationsrdquoApplied Mathematical Modelling vol 60 pp 164ndash178 2018

10 Mathematical Problems in Engineering

From the results in the above figure we can see that thedegree of centrality of node p3 is 9 the degree of centrality ofp4 is 7 and the standardization of the two nodes is 064286and 05 respectively It can be seen that the p3 node and thep4 node are relatively important During the spread ofWeChat epidemic-related information monitoring andguiding these two nodes has a great impact on the overallinformation spread

32 Key Node Recognition Method Based on WeChatSupernetwork Degree centrality is currently one of the mostcommonly used key node identification methods but itsapplication in a Supernetwork has deficiencies e degreecentrality calculation here does not distinguish which subneteach node belongs to in the Supernetwork there is nodistinction between the relationships between nodes andthere is no difference between the relationships betweensubnets Accordingly this method cannot reflect the con-nection status of a node in the subnet to which it belongsnor can it reflect the propagation ability of the node in thesubnet to which it belongs similarly in the current situationthis method also fails to reflect the connection status of anode between subnetworks and it fails to measure thepropagation ability of the node between subnetworks Re-ferring to Figures 3 and 4 for example the i1 node has adegree of centrality of

CD(i1) d(i1) 1113944j

Xij 1113944j

Xji 3 (3)

And the m3 node has a degree of centrality of

CD(m3) d(m3) 1113944j

Xij 1113944j

Xji 4 (4)

According to the formula

CDprime ni( 1113857

d ni( 1113857

g minus 1 (5)

e standardized degree of centrality of i1 can be ob-tained as

CDprime (i1)

d(i1)

g minus 1 021429 (6)

And the standardized degree of centrality of node m3 is

CDprime (m3)

d(m3)

g minus 1 028571 (7)

us node i1 is not as important as m3 but in theprocess of epidemic information propagation in WeChat inthe Supernetwork i1 is associated with three unary subnetswhile m3 is only associated with the M-M network and P-Pnetwork and is not directly connected to the I-I networkFrom this perspective i1 is more important than m3 espread of epidemic information in WeChat has uniquefeatures For example the ability of ordinary WeChat usersto spread information in the circle of friends is related to thenumber of their friends the ability of the public account tospread information in WeChat is related to the number of

fans and the ability to spread information inWeChat groupsand the number of WeChat group members is related enodes with strong propagation ability are more importantand the identificationmethods of these key nodes inWeChatneed to be rebuilt

In order to avoid the above deficiencies this paperproposes a new comprehensive method for identifying keynodes in WeChat epidemic information disseminationbased on a Supernetwork part of which is based on animprovement of the decision method proposed previously[13] and the other part is mainly constructed based on thecharacteristics of the spread of epidemic information inWeChat e new method is briefly described as follows

Let ni be any node in the Supernetwork QCD(ni)

represents the degree of centrality of ni in the entireSupernetwork and ZCD(ni) is the degree of centrality of ni

in the unary subnet to which it belongs

(1) Step 1 Calculate and compare the degree of cen-trality of each node in the entire Supernetwork

(2) Step 2 Calculate and compare the degree centralityof all nodes in the M-P binary subnetwork and theI-P binary subnetwork in the M-P binary subnet-work and I-P binary subnetwork to which theybelong

(3) Step 3 Calculate and compare the degree centralityof all the individuals in the entire Supernetworksystem in the subunit networks to which they belong

(4) Step 4 Calculate and compare the internetworkpropagation capabilities of each node in the subnet ofa unitary network in the Supernetwork Let LZS(ni)

be the number of unitary subnetworks connected bynode ni and ZJBS(ni) the edges of node ni betweenthe unitary subnetworks e number can be ob-tained from the above analysisZJBS(ni) QCD(ni) minus ZCD(ni) the network prop-agation ability of the node ni in the Supernetwork isexpressed by ZJCN(ni) and the calculation andcomparison methods are as follows

Select Case LZS(A)

Case ISgt LZS(B)

ZJCN(A)gtZJCN(B)

Case ISlt LZS(B)

ZJCN(A)ltZJCN(B)

Case IS LZS(B)

Select Case ZJBS(A)

Case ISgtZJBS(B)

ZJCN(A)gtZJCN(B)

Case ISltZJBS(B)

ZJCN(A)ltZJCN(B)

Case IS ZJBS(B)

ZJCN(A) ZJCN(B)

End SelectEnd Select

6 Mathematical Problems in Engineering

(5) Step 5 Calculate and compare the internetworkpropagation capability ZJCNJ(ni) between theM-type nodes in the M-P binary subnetwork and theI-type nodes in the I-P binary subnetwork under thecorresponding binary subnetwork view LetJMminusPCD(ni) represent the degree of centrality of ni inthe M-P binary subnetwork to which it belongs andlet JIminusPCD(ni) represent the degree of centrality of ni

in the I-P binary subnetwork to which it belongs andthe calculation method of ZJCNJ(ni) is as followsSelect Case ni

Case IS isinM

ZJCNJ(ni) JMminusPCD(ni) minus ZCD(ni)

Case IS isin I

ZJCNJ(ni) JIminusPCD(ni) minus ZCD(ni)

End Select(6) Combining the results of the above steps key nodes

are identified

In the above steps Step 2 prepares for the calculation andcomparison of the number of fans of the public account andthe number of members in the WeChat group is determinedin Step 5 Step 3 the calculation result can also obtain thenumber of friends of ordinary WeChat users in the circle offriends e circle of friends is one of the main channels forordinary users to disseminate information in WeChat enumber of friends in the circle of friends is an importantcriterion for identifying the ability of ordinaryWeChat usersto disseminate information Step 4 compares the unarysubnet internetwork propagation capabilities of each node inthe Supernetwork view by the number of unary subnetworksconnected by the nodes and the number of nodes connectedbetween the unary subnetworks A ranking table was createdshowing the strengths and weaknesses of the unary subnetrsquosinternetwork spreading ability under the Supernetworkvision Among them QCD(ni) can be obtained by Step 1ZCD(ni) can be obtained by Step 3 and the individualrsquosZJBS(ni) can be obtained by the difference between QCD(ni)

and ZCD(ni) of an individual Firstly it is judged based onthe number of unary subnetworks connected to the node

e number of unary subnetworks connected to node A isgreater than the number of unary subnetworks connected tonode B which indicates that the internetwork communi-cation capability of node A is stronger than that of node B Ifthe number of unary subnetworks connected to node A isless than the number of unary subnetworks connected tonode B it indicates that the internetwork propagation ca-pability of node A between unary subnetworks is weakerthan that of node B If the number of unary subnetworksconnected to node A is the same as the number of unarysubnetworks connected to node B further judgments needto be made based on the number of edges between the unarysubnetworks of nodes Step 5 is mainly based on the cal-culation results of Step 2 and Step 3 and calculates andcompares the number of fans of the public account and thenumber of members of the WeChat group in the WeChatSupernetwork e information dissemination ability ofnodes is measured to provide a reference for the identifi-cation of key nodes is step calculates the internetworkpropagation capability between theM-type nodes in theM-Pbinary subnetwork and the I-type nodes in the I-P binarysubnetwork from the binary subnetwork perspective

Taking the example shown in Figure 3 for verificationand analysis

(1) Step 1 e calculation result is shown in Figure 4(2) Step 2 e screenshots of the system calculation

results are shown in Figures 5 and 6(3) Step 3 e result is shown in Figure 7(4) Step 4 e results are shown in Table 1(5) Combining the comparison and calculation results

of Step 2 and Figures 5 and 6 with the comparisonand calculation results of Step 3 and Figure 7 thecalculation and comparison results of this step areshown in Tables 2 and 3

(6) From the perspective of intranetwork propagationFigure 7 shows that the degree of centrality of i3 i4and i5 in the I-I network is the same and the highestand the propagation ability of i3 i4 and i5 in thenetwork is also the strongest Nodesm1m2m3 and

8 9000 64286 01229 7000 50000 00954 6000

50005000

500050005000500040004000300030003000

42857 008110 35714

35714

35714357143571435714

12 i2671215 0068

006800680068

00685000 35714 0068

0068

3 2857128571 0054

00541413

2142921429

21429115 0041

00410041

Degree1

NrmDegree2

Share3

p3p4m4p5

p1p2m1m2

i3i4

i5

i1m5

m3

Figure 4 e degree of centrality of all nodes in the WeChat epidemic information Supernetwork

Mathematical Problems in Engineering 7

m4 have strong propagation capabilities in the M-Mnetwork In the P-P network p3 and p4 are thestrongest nodes in the network From the perspectiveof internetwork propagation Table 1 shows that thenumber of subnetworks connected by nodes p3 andi2 is larger and the number of interconnected edgesbetween networks is also larger so their internet-work propagation capabilities are stronger edegree centrality value of such nodes may not be

large but its influence on the propagation effect isoften large which is worthy of attention It can alsobe seen from Table 1 that although m3 has thestrongest propagation capability in the M-M net-work and i1 has the weakest propagation capabilityin the I-I network in Figure 7 from the perspective ofinternetwork propagation i1 connects three subnetsthere are 2 internetwork edges m3 only connects 2subnets and there is only 1 internetwork edge so i1

3 7000 77778 01754 5000

50004000400040004000300020002000

55556 01255 55556 01252 44444

444444444444444333332222222222

01007 010010 01009 01008 00751 00506 0050

Degree1

NrmDegree2

Share3

p3p4p5p2i2i5i4i3p1i1

Figure 5 e degree of centrality of all nodes in the I-P network

6000600060005000400040004000300020002000

666676666766667

014301430143

55556 0119444444444444444

009500950095

33333 007122222 0048

8 p34 m49 p46 p12 m21 m13 m37 p25 m510 p5 22222 0048

Degree1

NrmDegree2

Share3

Figure 6 e degree of centrality of all nodes in the M-P network

12345

34125

34521

m1m2m3m4m5

Degree1

30003000300030000000

NrmDegree2

0000

750007500075000

75000

Share3

0000

0250025002500250

p3p4p1p2p5

Degree1

40004000200020002000

2000

20002000

NrmDegree2

100000100000500005000050000

500005000050000

Share3

Degree1

NrmDegree2

Share3

02860286014301430143

10001000 25000

25000

02500250025001250125

i3i4i5i2i1

Figure 7 e degree of centrality of each node in the unary subnet to which it belongs

8 Mathematical Problems in Engineering

is slightly better than m3 in terms of internetworkcommunication capability From the perspective ofthe spread of epidemic-related information inWeChat Figure 7 shows that p3 and p4 have a strongability to spread epidemic-related information in theWeChat circle of friends Under the same conditionsthe spread of epidemic-related information of thesetwo ordinary user nodes is faster e spreadingrange is wide Table 2 shows that m4 has a strongspreading capability in WeChat group nodes Underthe same conditions the information spreadingspeed of this WeChat group node is faster and thespreading range is wider Table 3 shows i2 in thepublic account category e dissemination capa-bility of the node is strong Under the same con-ditions the public information nodersquos epidemic-related information spreads faster more widely Toguide the dissemination of epidemic-related infor-mation in WeChat it is best to guide the

abovementioned WeChat nodes with a strong abilityto disseminate epidemic-related information

e new method also identifies the importance of or-dinary WeChat users WeChat groups and official accountsfrom the perspective of information diffusion based on theparticularity of the spread of WeChat epidemic-relatedinformation in order to be more comprehensive andreasonable

4 Conclusions

is article mainly concerns the model construction and keynode identification of the WeChat epidemic-related infor-mation dissemination Supernetwork e identificationmethod can be roughly divided into two parts One part isbased on the improvement of the decision method proposedpreviously [13] and the other part of it is mainly based onthe characteristics of the spread of information related to the

Table 1 Sequence table of nodersquos internetwork epidemic information dissemination ability

Node Number of unary subnets associated Number of relationshipsp3 3 5i2 3 4p2 3 3p4 3 3i5 3 3m1 3 2i1 3 2m2 3 2m5 2 3p1 2 3m4 2 3p5 2 3i4 2 2m3 2 1i3 2 1

Table 3 Sorting table of the spreading capacity of epidemic information in WeChat for Class I nodes

Node Degree of centralitywithin the I-P network

Degree of centrality withinthe I-I network

Important indicators of WeChatepidemic information dissemination capability

i2 4 1 3i4 4 2 2i5 4 2 2i3 3 2 1i1 2 1 1

Table 2 Sorting table of M-type nodesrsquo epidemic information dissemination capability in WeChat

Node Degree of centralitywithin the M-P network

Degree centrality withinthe M-M network

Important indicators of WeChatepidemic information dissemination capability

m4 6 3 3m5 2 0 2m1 4 3 1m2 4 3 1m3 4 3 1

Mathematical Problems in Engineering 9

epidemic in WeChat e Supernetwork model of WeChatepidemic information dissemination and the correspondingkey node identification method constructed in this study arethe initial attempts to research the information dissemi-nation of epidemic-related information in WeChat

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

PengWu and Di Zhao contributed to the design of the studyPeng Wu gave the main idea of the manuscript wrote thefirst draft and performed the design of figures All authorscontributed to the manuscript revision and read and ap-proved the submitted version

Acknowledgments

is work was supported by the National Social ScienceFund Project (18BGL238) China the China PostdoctoralScience Foundation Special Funding Project (2018T110724)China the Chinese Postdoctoral Science Fund GeneralSupport Project (2016M602236) China and the HenanPhilosophy and Social Science Planning Project(2017BJJ021) and Key Research Project of Teacher Educa-tion Curriculum Reform in Henan Province (2018-JSJYZD-008) China

References

[1] Science Net ldquoMining social network opinion leadersrdquo 2020httpblogsciencenetcnhomephpmodspaceampuid3075ampdoblogampid466991

[2] Surging News ldquoe 2019 WeChat annual data report is outrdquo2020 httpswwwthepapercnnewsDetail_forward_5480482

[3] L L Liu ldquoResearch on new coronary pneumonia epidemicreports from the perspective of the frameworkrdquo JournalismLover vol 5 pp 17ndash21 2020

[4] Z Deng X J Liu and Z D Kang ldquoResearch on the publicopinion propaganda and ideological education function ofuniversity new media in the prevention and control of majorepidemicsrdquo Studies in Ideological Education no 3 pp 38ndash432020

[5] Y S Chen ldquoResearch on spreading and governance of in-ternet rumors on public health emergencyrdquo E-Governmentno 6 pp 2ndash11 2020

[6] B J Wan C Guo Z Zhao et al ldquoCharacteristics and risksreflections of ldquoanti-epidemic fitness messagesrdquo delivered byWeChat during the COVID-19 epidemicrdquo Journal of XirsquoanPhysical Education University vol 37 no 3 pp 267ndash2752020

[7] Y Lu and L Zhang ldquoSocial media WeChat infers the de-velopment trend of COVID-19rdquo Journal of Infection no 81pp 82-83 2020

[8] A Nagurney and J Dong SupernetworksDecision-Making forthe Information Age Edward Elgar Publishing CheltenhamUK 2002

[9] Z P Wang and Z T Wang Supernetwork eory and itsApplication Science Press Beijing China 2008

[10] A Nagurney ldquoOptimal supply chain network design andredesign at minimal total cost and with demand satisfactionrdquoInternational Journal of Production Economics vol 128 no 1pp 200ndash208 2010

[11] A Nagurney M Yu and Q Qiang ldquoSupply chain networkdesign for critical needs with outsourcingrdquo Papers in RegionalScience vol 90 no 1 pp 123ndash142 2011

[12] L Zhu and J Cao ldquoSupernetwork optimization of emergencyresources allocation under disaster riskrdquo Chinese Journal ofManagement Science vol 20 no 6 pp 141ndash148 2012

[13] P Wu and H S Wang ldquoModeling of information dissemi-nation supernetwork in the emergencies and determination ofthe important nodes in the supernetworkrdquo Journal of theChina Society for Scientific and Technical Information vol 37no 7 pp 722ndash729 2012

[14] Y J Xi Y Z Dang and K J Liao ldquoKnowledge supernetworkmodel and its application in organizational knowledge sys-temsrdquo Journal of Management Sciences in China vol 12 no 3pp 12ndash21 2009

[15] P Wu H S Wang Y Li et al ldquoJudgment of importantcontrol nodes in the information dissemination super-net-work of emergencyrdquo Library and Information Service vol 57no 1 pp 112ndash116 2013

[16] Y Yu Research on Knowledge Supernetwork in OrganizationalKnowledge Management Dalian University of TechnologyDalian China 2009

[17] J L Segovia-juarez S Colombano and D KirschnerldquoIdentifying DNA splice sites using hypernetworks with ar-tificial molecular evolutionrdquo Biosystems vol 87 no 2-3pp 117ndash124 2007

[18] Z T Wang ldquoReflection on supernetworkrdquo Journal of Uni-versity of Shanghai for Science and Technology vol 33 no 3pp 229ndash237 2011

[19] J-B Liu J Cao A Alofi A AL-Mazrooei and A ElaiwldquoApplications of laplacian spectra for n-prism networksrdquoNeurocomputing vol 198 pp 69ndash73 2016

[20] J D Luo Lecture Notes on Social Network Analysis SocialSciences Academic Press Beijing China 2nd edition 2010

[21] S Hayat S Wang and J-B Liu ldquoValency-based topologicaldescriptors of chemical networks and their applicationsrdquoApplied Mathematical Modelling vol 60 pp 164ndash178 2018

10 Mathematical Problems in Engineering

(5) Step 5 Calculate and compare the internetworkpropagation capability ZJCNJ(ni) between theM-type nodes in the M-P binary subnetwork and theI-type nodes in the I-P binary subnetwork under thecorresponding binary subnetwork view LetJMminusPCD(ni) represent the degree of centrality of ni inthe M-P binary subnetwork to which it belongs andlet JIminusPCD(ni) represent the degree of centrality of ni

in the I-P binary subnetwork to which it belongs andthe calculation method of ZJCNJ(ni) is as followsSelect Case ni

Case IS isinM

ZJCNJ(ni) JMminusPCD(ni) minus ZCD(ni)

Case IS isin I

ZJCNJ(ni) JIminusPCD(ni) minus ZCD(ni)

End Select(6) Combining the results of the above steps key nodes

are identified

In the above steps Step 2 prepares for the calculation andcomparison of the number of fans of the public account andthe number of members in the WeChat group is determinedin Step 5 Step 3 the calculation result can also obtain thenumber of friends of ordinary WeChat users in the circle offriends e circle of friends is one of the main channels forordinary users to disseminate information in WeChat enumber of friends in the circle of friends is an importantcriterion for identifying the ability of ordinaryWeChat usersto disseminate information Step 4 compares the unarysubnet internetwork propagation capabilities of each node inthe Supernetwork view by the number of unary subnetworksconnected by the nodes and the number of nodes connectedbetween the unary subnetworks A ranking table was createdshowing the strengths and weaknesses of the unary subnetrsquosinternetwork spreading ability under the Supernetworkvision Among them QCD(ni) can be obtained by Step 1ZCD(ni) can be obtained by Step 3 and the individualrsquosZJBS(ni) can be obtained by the difference between QCD(ni)

and ZCD(ni) of an individual Firstly it is judged based onthe number of unary subnetworks connected to the node

e number of unary subnetworks connected to node A isgreater than the number of unary subnetworks connected tonode B which indicates that the internetwork communi-cation capability of node A is stronger than that of node B Ifthe number of unary subnetworks connected to node A isless than the number of unary subnetworks connected tonode B it indicates that the internetwork propagation ca-pability of node A between unary subnetworks is weakerthan that of node B If the number of unary subnetworksconnected to node A is the same as the number of unarysubnetworks connected to node B further judgments needto be made based on the number of edges between the unarysubnetworks of nodes Step 5 is mainly based on the cal-culation results of Step 2 and Step 3 and calculates andcompares the number of fans of the public account and thenumber of members of the WeChat group in the WeChatSupernetwork e information dissemination ability ofnodes is measured to provide a reference for the identifi-cation of key nodes is step calculates the internetworkpropagation capability between theM-type nodes in theM-Pbinary subnetwork and the I-type nodes in the I-P binarysubnetwork from the binary subnetwork perspective

Taking the example shown in Figure 3 for verificationand analysis

(1) Step 1 e calculation result is shown in Figure 4(2) Step 2 e screenshots of the system calculation

results are shown in Figures 5 and 6(3) Step 3 e result is shown in Figure 7(4) Step 4 e results are shown in Table 1(5) Combining the comparison and calculation results

of Step 2 and Figures 5 and 6 with the comparisonand calculation results of Step 3 and Figure 7 thecalculation and comparison results of this step areshown in Tables 2 and 3

(6) From the perspective of intranetwork propagationFigure 7 shows that the degree of centrality of i3 i4and i5 in the I-I network is the same and the highestand the propagation ability of i3 i4 and i5 in thenetwork is also the strongest Nodesm1m2m3 and

8 9000 64286 01229 7000 50000 00954 6000

50005000

500050005000500040004000300030003000

42857 008110 35714

35714

35714357143571435714

12 i2671215 0068

006800680068

00685000 35714 0068

0068

3 2857128571 0054

00541413

2142921429

21429115 0041

00410041

Degree1

NrmDegree2

Share3

p3p4m4p5

p1p2m1m2

i3i4

i5

i1m5

m3

Figure 4 e degree of centrality of all nodes in the WeChat epidemic information Supernetwork

Mathematical Problems in Engineering 7

m4 have strong propagation capabilities in the M-Mnetwork In the P-P network p3 and p4 are thestrongest nodes in the network From the perspectiveof internetwork propagation Table 1 shows that thenumber of subnetworks connected by nodes p3 andi2 is larger and the number of interconnected edgesbetween networks is also larger so their internet-work propagation capabilities are stronger edegree centrality value of such nodes may not be

large but its influence on the propagation effect isoften large which is worthy of attention It can alsobe seen from Table 1 that although m3 has thestrongest propagation capability in the M-M net-work and i1 has the weakest propagation capabilityin the I-I network in Figure 7 from the perspective ofinternetwork propagation i1 connects three subnetsthere are 2 internetwork edges m3 only connects 2subnets and there is only 1 internetwork edge so i1

3 7000 77778 01754 5000

50004000400040004000300020002000

55556 01255 55556 01252 44444

444444444444444333332222222222

01007 010010 01009 01008 00751 00506 0050

Degree1

NrmDegree2

Share3

p3p4p5p2i2i5i4i3p1i1

Figure 5 e degree of centrality of all nodes in the I-P network

6000600060005000400040004000300020002000

666676666766667

014301430143

55556 0119444444444444444

009500950095

33333 007122222 0048

8 p34 m49 p46 p12 m21 m13 m37 p25 m510 p5 22222 0048

Degree1

NrmDegree2

Share3

Figure 6 e degree of centrality of all nodes in the M-P network

12345

34125

34521

m1m2m3m4m5

Degree1

30003000300030000000

NrmDegree2

0000

750007500075000

75000

Share3

0000

0250025002500250

p3p4p1p2p5

Degree1

40004000200020002000

2000

20002000

NrmDegree2

100000100000500005000050000

500005000050000

Share3

Degree1

NrmDegree2

Share3

02860286014301430143

10001000 25000

25000

02500250025001250125

i3i4i5i2i1

Figure 7 e degree of centrality of each node in the unary subnet to which it belongs

8 Mathematical Problems in Engineering

is slightly better than m3 in terms of internetworkcommunication capability From the perspective ofthe spread of epidemic-related information inWeChat Figure 7 shows that p3 and p4 have a strongability to spread epidemic-related information in theWeChat circle of friends Under the same conditionsthe spread of epidemic-related information of thesetwo ordinary user nodes is faster e spreadingrange is wide Table 2 shows that m4 has a strongspreading capability in WeChat group nodes Underthe same conditions the information spreadingspeed of this WeChat group node is faster and thespreading range is wider Table 3 shows i2 in thepublic account category e dissemination capa-bility of the node is strong Under the same con-ditions the public information nodersquos epidemic-related information spreads faster more widely Toguide the dissemination of epidemic-related infor-mation in WeChat it is best to guide the

abovementioned WeChat nodes with a strong abilityto disseminate epidemic-related information

e new method also identifies the importance of or-dinary WeChat users WeChat groups and official accountsfrom the perspective of information diffusion based on theparticularity of the spread of WeChat epidemic-relatedinformation in order to be more comprehensive andreasonable

4 Conclusions

is article mainly concerns the model construction and keynode identification of the WeChat epidemic-related infor-mation dissemination Supernetwork e identificationmethod can be roughly divided into two parts One part isbased on the improvement of the decision method proposedpreviously [13] and the other part of it is mainly based onthe characteristics of the spread of information related to the

Table 1 Sequence table of nodersquos internetwork epidemic information dissemination ability

Node Number of unary subnets associated Number of relationshipsp3 3 5i2 3 4p2 3 3p4 3 3i5 3 3m1 3 2i1 3 2m2 3 2m5 2 3p1 2 3m4 2 3p5 2 3i4 2 2m3 2 1i3 2 1

Table 3 Sorting table of the spreading capacity of epidemic information in WeChat for Class I nodes

Node Degree of centralitywithin the I-P network

Degree of centrality withinthe I-I network

Important indicators of WeChatepidemic information dissemination capability

i2 4 1 3i4 4 2 2i5 4 2 2i3 3 2 1i1 2 1 1

Table 2 Sorting table of M-type nodesrsquo epidemic information dissemination capability in WeChat

Node Degree of centralitywithin the M-P network

Degree centrality withinthe M-M network

Important indicators of WeChatepidemic information dissemination capability

m4 6 3 3m5 2 0 2m1 4 3 1m2 4 3 1m3 4 3 1

Mathematical Problems in Engineering 9

epidemic in WeChat e Supernetwork model of WeChatepidemic information dissemination and the correspondingkey node identification method constructed in this study arethe initial attempts to research the information dissemi-nation of epidemic-related information in WeChat

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

PengWu and Di Zhao contributed to the design of the studyPeng Wu gave the main idea of the manuscript wrote thefirst draft and performed the design of figures All authorscontributed to the manuscript revision and read and ap-proved the submitted version

Acknowledgments

is work was supported by the National Social ScienceFund Project (18BGL238) China the China PostdoctoralScience Foundation Special Funding Project (2018T110724)China the Chinese Postdoctoral Science Fund GeneralSupport Project (2016M602236) China and the HenanPhilosophy and Social Science Planning Project(2017BJJ021) and Key Research Project of Teacher Educa-tion Curriculum Reform in Henan Province (2018-JSJYZD-008) China

References

[1] Science Net ldquoMining social network opinion leadersrdquo 2020httpblogsciencenetcnhomephpmodspaceampuid3075ampdoblogampid466991

[2] Surging News ldquoe 2019 WeChat annual data report is outrdquo2020 httpswwwthepapercnnewsDetail_forward_5480482

[3] L L Liu ldquoResearch on new coronary pneumonia epidemicreports from the perspective of the frameworkrdquo JournalismLover vol 5 pp 17ndash21 2020

[4] Z Deng X J Liu and Z D Kang ldquoResearch on the publicopinion propaganda and ideological education function ofuniversity new media in the prevention and control of majorepidemicsrdquo Studies in Ideological Education no 3 pp 38ndash432020

[5] Y S Chen ldquoResearch on spreading and governance of in-ternet rumors on public health emergencyrdquo E-Governmentno 6 pp 2ndash11 2020

[6] B J Wan C Guo Z Zhao et al ldquoCharacteristics and risksreflections of ldquoanti-epidemic fitness messagesrdquo delivered byWeChat during the COVID-19 epidemicrdquo Journal of XirsquoanPhysical Education University vol 37 no 3 pp 267ndash2752020

[7] Y Lu and L Zhang ldquoSocial media WeChat infers the de-velopment trend of COVID-19rdquo Journal of Infection no 81pp 82-83 2020

[8] A Nagurney and J Dong SupernetworksDecision-Making forthe Information Age Edward Elgar Publishing CheltenhamUK 2002

[9] Z P Wang and Z T Wang Supernetwork eory and itsApplication Science Press Beijing China 2008

[10] A Nagurney ldquoOptimal supply chain network design andredesign at minimal total cost and with demand satisfactionrdquoInternational Journal of Production Economics vol 128 no 1pp 200ndash208 2010

[11] A Nagurney M Yu and Q Qiang ldquoSupply chain networkdesign for critical needs with outsourcingrdquo Papers in RegionalScience vol 90 no 1 pp 123ndash142 2011

[12] L Zhu and J Cao ldquoSupernetwork optimization of emergencyresources allocation under disaster riskrdquo Chinese Journal ofManagement Science vol 20 no 6 pp 141ndash148 2012

[13] P Wu and H S Wang ldquoModeling of information dissemi-nation supernetwork in the emergencies and determination ofthe important nodes in the supernetworkrdquo Journal of theChina Society for Scientific and Technical Information vol 37no 7 pp 722ndash729 2012

[14] Y J Xi Y Z Dang and K J Liao ldquoKnowledge supernetworkmodel and its application in organizational knowledge sys-temsrdquo Journal of Management Sciences in China vol 12 no 3pp 12ndash21 2009

[15] P Wu H S Wang Y Li et al ldquoJudgment of importantcontrol nodes in the information dissemination super-net-work of emergencyrdquo Library and Information Service vol 57no 1 pp 112ndash116 2013

[16] Y Yu Research on Knowledge Supernetwork in OrganizationalKnowledge Management Dalian University of TechnologyDalian China 2009

[17] J L Segovia-juarez S Colombano and D KirschnerldquoIdentifying DNA splice sites using hypernetworks with ar-tificial molecular evolutionrdquo Biosystems vol 87 no 2-3pp 117ndash124 2007

[18] Z T Wang ldquoReflection on supernetworkrdquo Journal of Uni-versity of Shanghai for Science and Technology vol 33 no 3pp 229ndash237 2011

[19] J-B Liu J Cao A Alofi A AL-Mazrooei and A ElaiwldquoApplications of laplacian spectra for n-prism networksrdquoNeurocomputing vol 198 pp 69ndash73 2016

[20] J D Luo Lecture Notes on Social Network Analysis SocialSciences Academic Press Beijing China 2nd edition 2010

[21] S Hayat S Wang and J-B Liu ldquoValency-based topologicaldescriptors of chemical networks and their applicationsrdquoApplied Mathematical Modelling vol 60 pp 164ndash178 2018

10 Mathematical Problems in Engineering

m4 have strong propagation capabilities in the M-Mnetwork In the P-P network p3 and p4 are thestrongest nodes in the network From the perspectiveof internetwork propagation Table 1 shows that thenumber of subnetworks connected by nodes p3 andi2 is larger and the number of interconnected edgesbetween networks is also larger so their internet-work propagation capabilities are stronger edegree centrality value of such nodes may not be

large but its influence on the propagation effect isoften large which is worthy of attention It can alsobe seen from Table 1 that although m3 has thestrongest propagation capability in the M-M net-work and i1 has the weakest propagation capabilityin the I-I network in Figure 7 from the perspective ofinternetwork propagation i1 connects three subnetsthere are 2 internetwork edges m3 only connects 2subnets and there is only 1 internetwork edge so i1

3 7000 77778 01754 5000

50004000400040004000300020002000

55556 01255 55556 01252 44444

444444444444444333332222222222

01007 010010 01009 01008 00751 00506 0050

Degree1

NrmDegree2

Share3

p3p4p5p2i2i5i4i3p1i1

Figure 5 e degree of centrality of all nodes in the I-P network

6000600060005000400040004000300020002000

666676666766667

014301430143

55556 0119444444444444444

009500950095

33333 007122222 0048

8 p34 m49 p46 p12 m21 m13 m37 p25 m510 p5 22222 0048

Degree1

NrmDegree2

Share3

Figure 6 e degree of centrality of all nodes in the M-P network

12345

34125

34521

m1m2m3m4m5

Degree1

30003000300030000000

NrmDegree2

0000

750007500075000

75000

Share3

0000

0250025002500250

p3p4p1p2p5

Degree1

40004000200020002000

2000

20002000

NrmDegree2

100000100000500005000050000

500005000050000

Share3

Degree1

NrmDegree2

Share3

02860286014301430143

10001000 25000

25000

02500250025001250125

i3i4i5i2i1

Figure 7 e degree of centrality of each node in the unary subnet to which it belongs

8 Mathematical Problems in Engineering

is slightly better than m3 in terms of internetworkcommunication capability From the perspective ofthe spread of epidemic-related information inWeChat Figure 7 shows that p3 and p4 have a strongability to spread epidemic-related information in theWeChat circle of friends Under the same conditionsthe spread of epidemic-related information of thesetwo ordinary user nodes is faster e spreadingrange is wide Table 2 shows that m4 has a strongspreading capability in WeChat group nodes Underthe same conditions the information spreadingspeed of this WeChat group node is faster and thespreading range is wider Table 3 shows i2 in thepublic account category e dissemination capa-bility of the node is strong Under the same con-ditions the public information nodersquos epidemic-related information spreads faster more widely Toguide the dissemination of epidemic-related infor-mation in WeChat it is best to guide the

abovementioned WeChat nodes with a strong abilityto disseminate epidemic-related information

e new method also identifies the importance of or-dinary WeChat users WeChat groups and official accountsfrom the perspective of information diffusion based on theparticularity of the spread of WeChat epidemic-relatedinformation in order to be more comprehensive andreasonable

4 Conclusions

is article mainly concerns the model construction and keynode identification of the WeChat epidemic-related infor-mation dissemination Supernetwork e identificationmethod can be roughly divided into two parts One part isbased on the improvement of the decision method proposedpreviously [13] and the other part of it is mainly based onthe characteristics of the spread of information related to the

Table 1 Sequence table of nodersquos internetwork epidemic information dissemination ability

Node Number of unary subnets associated Number of relationshipsp3 3 5i2 3 4p2 3 3p4 3 3i5 3 3m1 3 2i1 3 2m2 3 2m5 2 3p1 2 3m4 2 3p5 2 3i4 2 2m3 2 1i3 2 1

Table 3 Sorting table of the spreading capacity of epidemic information in WeChat for Class I nodes

Node Degree of centralitywithin the I-P network

Degree of centrality withinthe I-I network

Important indicators of WeChatepidemic information dissemination capability

i2 4 1 3i4 4 2 2i5 4 2 2i3 3 2 1i1 2 1 1

Table 2 Sorting table of M-type nodesrsquo epidemic information dissemination capability in WeChat

Node Degree of centralitywithin the M-P network

Degree centrality withinthe M-M network

Important indicators of WeChatepidemic information dissemination capability

m4 6 3 3m5 2 0 2m1 4 3 1m2 4 3 1m3 4 3 1

Mathematical Problems in Engineering 9

epidemic in WeChat e Supernetwork model of WeChatepidemic information dissemination and the correspondingkey node identification method constructed in this study arethe initial attempts to research the information dissemi-nation of epidemic-related information in WeChat

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

PengWu and Di Zhao contributed to the design of the studyPeng Wu gave the main idea of the manuscript wrote thefirst draft and performed the design of figures All authorscontributed to the manuscript revision and read and ap-proved the submitted version

Acknowledgments

is work was supported by the National Social ScienceFund Project (18BGL238) China the China PostdoctoralScience Foundation Special Funding Project (2018T110724)China the Chinese Postdoctoral Science Fund GeneralSupport Project (2016M602236) China and the HenanPhilosophy and Social Science Planning Project(2017BJJ021) and Key Research Project of Teacher Educa-tion Curriculum Reform in Henan Province (2018-JSJYZD-008) China

References

[1] Science Net ldquoMining social network opinion leadersrdquo 2020httpblogsciencenetcnhomephpmodspaceampuid3075ampdoblogampid466991

[2] Surging News ldquoe 2019 WeChat annual data report is outrdquo2020 httpswwwthepapercnnewsDetail_forward_5480482

[3] L L Liu ldquoResearch on new coronary pneumonia epidemicreports from the perspective of the frameworkrdquo JournalismLover vol 5 pp 17ndash21 2020

[4] Z Deng X J Liu and Z D Kang ldquoResearch on the publicopinion propaganda and ideological education function ofuniversity new media in the prevention and control of majorepidemicsrdquo Studies in Ideological Education no 3 pp 38ndash432020

[5] Y S Chen ldquoResearch on spreading and governance of in-ternet rumors on public health emergencyrdquo E-Governmentno 6 pp 2ndash11 2020

[6] B J Wan C Guo Z Zhao et al ldquoCharacteristics and risksreflections of ldquoanti-epidemic fitness messagesrdquo delivered byWeChat during the COVID-19 epidemicrdquo Journal of XirsquoanPhysical Education University vol 37 no 3 pp 267ndash2752020

[7] Y Lu and L Zhang ldquoSocial media WeChat infers the de-velopment trend of COVID-19rdquo Journal of Infection no 81pp 82-83 2020

[8] A Nagurney and J Dong SupernetworksDecision-Making forthe Information Age Edward Elgar Publishing CheltenhamUK 2002

[9] Z P Wang and Z T Wang Supernetwork eory and itsApplication Science Press Beijing China 2008

[10] A Nagurney ldquoOptimal supply chain network design andredesign at minimal total cost and with demand satisfactionrdquoInternational Journal of Production Economics vol 128 no 1pp 200ndash208 2010

[11] A Nagurney M Yu and Q Qiang ldquoSupply chain networkdesign for critical needs with outsourcingrdquo Papers in RegionalScience vol 90 no 1 pp 123ndash142 2011

[12] L Zhu and J Cao ldquoSupernetwork optimization of emergencyresources allocation under disaster riskrdquo Chinese Journal ofManagement Science vol 20 no 6 pp 141ndash148 2012

[13] P Wu and H S Wang ldquoModeling of information dissemi-nation supernetwork in the emergencies and determination ofthe important nodes in the supernetworkrdquo Journal of theChina Society for Scientific and Technical Information vol 37no 7 pp 722ndash729 2012

[14] Y J Xi Y Z Dang and K J Liao ldquoKnowledge supernetworkmodel and its application in organizational knowledge sys-temsrdquo Journal of Management Sciences in China vol 12 no 3pp 12ndash21 2009

[15] P Wu H S Wang Y Li et al ldquoJudgment of importantcontrol nodes in the information dissemination super-net-work of emergencyrdquo Library and Information Service vol 57no 1 pp 112ndash116 2013

[16] Y Yu Research on Knowledge Supernetwork in OrganizationalKnowledge Management Dalian University of TechnologyDalian China 2009

[17] J L Segovia-juarez S Colombano and D KirschnerldquoIdentifying DNA splice sites using hypernetworks with ar-tificial molecular evolutionrdquo Biosystems vol 87 no 2-3pp 117ndash124 2007

[18] Z T Wang ldquoReflection on supernetworkrdquo Journal of Uni-versity of Shanghai for Science and Technology vol 33 no 3pp 229ndash237 2011

[19] J-B Liu J Cao A Alofi A AL-Mazrooei and A ElaiwldquoApplications of laplacian spectra for n-prism networksrdquoNeurocomputing vol 198 pp 69ndash73 2016

[20] J D Luo Lecture Notes on Social Network Analysis SocialSciences Academic Press Beijing China 2nd edition 2010

[21] S Hayat S Wang and J-B Liu ldquoValency-based topologicaldescriptors of chemical networks and their applicationsrdquoApplied Mathematical Modelling vol 60 pp 164ndash178 2018

10 Mathematical Problems in Engineering

is slightly better than m3 in terms of internetworkcommunication capability From the perspective ofthe spread of epidemic-related information inWeChat Figure 7 shows that p3 and p4 have a strongability to spread epidemic-related information in theWeChat circle of friends Under the same conditionsthe spread of epidemic-related information of thesetwo ordinary user nodes is faster e spreadingrange is wide Table 2 shows that m4 has a strongspreading capability in WeChat group nodes Underthe same conditions the information spreadingspeed of this WeChat group node is faster and thespreading range is wider Table 3 shows i2 in thepublic account category e dissemination capa-bility of the node is strong Under the same con-ditions the public information nodersquos epidemic-related information spreads faster more widely Toguide the dissemination of epidemic-related infor-mation in WeChat it is best to guide the

abovementioned WeChat nodes with a strong abilityto disseminate epidemic-related information

e new method also identifies the importance of or-dinary WeChat users WeChat groups and official accountsfrom the perspective of information diffusion based on theparticularity of the spread of WeChat epidemic-relatedinformation in order to be more comprehensive andreasonable

4 Conclusions

is article mainly concerns the model construction and keynode identification of the WeChat epidemic-related infor-mation dissemination Supernetwork e identificationmethod can be roughly divided into two parts One part isbased on the improvement of the decision method proposedpreviously [13] and the other part of it is mainly based onthe characteristics of the spread of information related to the

Table 1 Sequence table of nodersquos internetwork epidemic information dissemination ability

Node Number of unary subnets associated Number of relationshipsp3 3 5i2 3 4p2 3 3p4 3 3i5 3 3m1 3 2i1 3 2m2 3 2m5 2 3p1 2 3m4 2 3p5 2 3i4 2 2m3 2 1i3 2 1

Table 3 Sorting table of the spreading capacity of epidemic information in WeChat for Class I nodes

Node Degree of centralitywithin the I-P network

Degree of centrality withinthe I-I network

Important indicators of WeChatepidemic information dissemination capability

i2 4 1 3i4 4 2 2i5 4 2 2i3 3 2 1i1 2 1 1

Table 2 Sorting table of M-type nodesrsquo epidemic information dissemination capability in WeChat

Node Degree of centralitywithin the M-P network

Degree centrality withinthe M-M network

Important indicators of WeChatepidemic information dissemination capability

m4 6 3 3m5 2 0 2m1 4 3 1m2 4 3 1m3 4 3 1

Mathematical Problems in Engineering 9

epidemic in WeChat e Supernetwork model of WeChatepidemic information dissemination and the correspondingkey node identification method constructed in this study arethe initial attempts to research the information dissemi-nation of epidemic-related information in WeChat

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

PengWu and Di Zhao contributed to the design of the studyPeng Wu gave the main idea of the manuscript wrote thefirst draft and performed the design of figures All authorscontributed to the manuscript revision and read and ap-proved the submitted version

Acknowledgments

is work was supported by the National Social ScienceFund Project (18BGL238) China the China PostdoctoralScience Foundation Special Funding Project (2018T110724)China the Chinese Postdoctoral Science Fund GeneralSupport Project (2016M602236) China and the HenanPhilosophy and Social Science Planning Project(2017BJJ021) and Key Research Project of Teacher Educa-tion Curriculum Reform in Henan Province (2018-JSJYZD-008) China

References

[1] Science Net ldquoMining social network opinion leadersrdquo 2020httpblogsciencenetcnhomephpmodspaceampuid3075ampdoblogampid466991

[2] Surging News ldquoe 2019 WeChat annual data report is outrdquo2020 httpswwwthepapercnnewsDetail_forward_5480482

[3] L L Liu ldquoResearch on new coronary pneumonia epidemicreports from the perspective of the frameworkrdquo JournalismLover vol 5 pp 17ndash21 2020

[4] Z Deng X J Liu and Z D Kang ldquoResearch on the publicopinion propaganda and ideological education function ofuniversity new media in the prevention and control of majorepidemicsrdquo Studies in Ideological Education no 3 pp 38ndash432020

[5] Y S Chen ldquoResearch on spreading and governance of in-ternet rumors on public health emergencyrdquo E-Governmentno 6 pp 2ndash11 2020

[6] B J Wan C Guo Z Zhao et al ldquoCharacteristics and risksreflections of ldquoanti-epidemic fitness messagesrdquo delivered byWeChat during the COVID-19 epidemicrdquo Journal of XirsquoanPhysical Education University vol 37 no 3 pp 267ndash2752020

[7] Y Lu and L Zhang ldquoSocial media WeChat infers the de-velopment trend of COVID-19rdquo Journal of Infection no 81pp 82-83 2020

[8] A Nagurney and J Dong SupernetworksDecision-Making forthe Information Age Edward Elgar Publishing CheltenhamUK 2002

[9] Z P Wang and Z T Wang Supernetwork eory and itsApplication Science Press Beijing China 2008

[10] A Nagurney ldquoOptimal supply chain network design andredesign at minimal total cost and with demand satisfactionrdquoInternational Journal of Production Economics vol 128 no 1pp 200ndash208 2010

[11] A Nagurney M Yu and Q Qiang ldquoSupply chain networkdesign for critical needs with outsourcingrdquo Papers in RegionalScience vol 90 no 1 pp 123ndash142 2011

[12] L Zhu and J Cao ldquoSupernetwork optimization of emergencyresources allocation under disaster riskrdquo Chinese Journal ofManagement Science vol 20 no 6 pp 141ndash148 2012

[13] P Wu and H S Wang ldquoModeling of information dissemi-nation supernetwork in the emergencies and determination ofthe important nodes in the supernetworkrdquo Journal of theChina Society for Scientific and Technical Information vol 37no 7 pp 722ndash729 2012

[14] Y J Xi Y Z Dang and K J Liao ldquoKnowledge supernetworkmodel and its application in organizational knowledge sys-temsrdquo Journal of Management Sciences in China vol 12 no 3pp 12ndash21 2009

[15] P Wu H S Wang Y Li et al ldquoJudgment of importantcontrol nodes in the information dissemination super-net-work of emergencyrdquo Library and Information Service vol 57no 1 pp 112ndash116 2013

[16] Y Yu Research on Knowledge Supernetwork in OrganizationalKnowledge Management Dalian University of TechnologyDalian China 2009

[17] J L Segovia-juarez S Colombano and D KirschnerldquoIdentifying DNA splice sites using hypernetworks with ar-tificial molecular evolutionrdquo Biosystems vol 87 no 2-3pp 117ndash124 2007

[18] Z T Wang ldquoReflection on supernetworkrdquo Journal of Uni-versity of Shanghai for Science and Technology vol 33 no 3pp 229ndash237 2011

[19] J-B Liu J Cao A Alofi A AL-Mazrooei and A ElaiwldquoApplications of laplacian spectra for n-prism networksrdquoNeurocomputing vol 198 pp 69ndash73 2016

[20] J D Luo Lecture Notes on Social Network Analysis SocialSciences Academic Press Beijing China 2nd edition 2010

[21] S Hayat S Wang and J-B Liu ldquoValency-based topologicaldescriptors of chemical networks and their applicationsrdquoApplied Mathematical Modelling vol 60 pp 164ndash178 2018

10 Mathematical Problems in Engineering

epidemic in WeChat e Supernetwork model of WeChatepidemic information dissemination and the correspondingkey node identification method constructed in this study arethe initial attempts to research the information dissemi-nation of epidemic-related information in WeChat

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

PengWu and Di Zhao contributed to the design of the studyPeng Wu gave the main idea of the manuscript wrote thefirst draft and performed the design of figures All authorscontributed to the manuscript revision and read and ap-proved the submitted version

Acknowledgments

is work was supported by the National Social ScienceFund Project (18BGL238) China the China PostdoctoralScience Foundation Special Funding Project (2018T110724)China the Chinese Postdoctoral Science Fund GeneralSupport Project (2016M602236) China and the HenanPhilosophy and Social Science Planning Project(2017BJJ021) and Key Research Project of Teacher Educa-tion Curriculum Reform in Henan Province (2018-JSJYZD-008) China

References

[1] Science Net ldquoMining social network opinion leadersrdquo 2020httpblogsciencenetcnhomephpmodspaceampuid3075ampdoblogampid466991

[2] Surging News ldquoe 2019 WeChat annual data report is outrdquo2020 httpswwwthepapercnnewsDetail_forward_5480482

[3] L L Liu ldquoResearch on new coronary pneumonia epidemicreports from the perspective of the frameworkrdquo JournalismLover vol 5 pp 17ndash21 2020

[4] Z Deng X J Liu and Z D Kang ldquoResearch on the publicopinion propaganda and ideological education function ofuniversity new media in the prevention and control of majorepidemicsrdquo Studies in Ideological Education no 3 pp 38ndash432020

[5] Y S Chen ldquoResearch on spreading and governance of in-ternet rumors on public health emergencyrdquo E-Governmentno 6 pp 2ndash11 2020

[6] B J Wan C Guo Z Zhao et al ldquoCharacteristics and risksreflections of ldquoanti-epidemic fitness messagesrdquo delivered byWeChat during the COVID-19 epidemicrdquo Journal of XirsquoanPhysical Education University vol 37 no 3 pp 267ndash2752020

[7] Y Lu and L Zhang ldquoSocial media WeChat infers the de-velopment trend of COVID-19rdquo Journal of Infection no 81pp 82-83 2020

[8] A Nagurney and J Dong SupernetworksDecision-Making forthe Information Age Edward Elgar Publishing CheltenhamUK 2002

[9] Z P Wang and Z T Wang Supernetwork eory and itsApplication Science Press Beijing China 2008

[10] A Nagurney ldquoOptimal supply chain network design andredesign at minimal total cost and with demand satisfactionrdquoInternational Journal of Production Economics vol 128 no 1pp 200ndash208 2010

[11] A Nagurney M Yu and Q Qiang ldquoSupply chain networkdesign for critical needs with outsourcingrdquo Papers in RegionalScience vol 90 no 1 pp 123ndash142 2011

[12] L Zhu and J Cao ldquoSupernetwork optimization of emergencyresources allocation under disaster riskrdquo Chinese Journal ofManagement Science vol 20 no 6 pp 141ndash148 2012

[13] P Wu and H S Wang ldquoModeling of information dissemi-nation supernetwork in the emergencies and determination ofthe important nodes in the supernetworkrdquo Journal of theChina Society for Scientific and Technical Information vol 37no 7 pp 722ndash729 2012

[14] Y J Xi Y Z Dang and K J Liao ldquoKnowledge supernetworkmodel and its application in organizational knowledge sys-temsrdquo Journal of Management Sciences in China vol 12 no 3pp 12ndash21 2009

[15] P Wu H S Wang Y Li et al ldquoJudgment of importantcontrol nodes in the information dissemination super-net-work of emergencyrdquo Library and Information Service vol 57no 1 pp 112ndash116 2013

[16] Y Yu Research on Knowledge Supernetwork in OrganizationalKnowledge Management Dalian University of TechnologyDalian China 2009

[17] J L Segovia-juarez S Colombano and D KirschnerldquoIdentifying DNA splice sites using hypernetworks with ar-tificial molecular evolutionrdquo Biosystems vol 87 no 2-3pp 117ndash124 2007

[18] Z T Wang ldquoReflection on supernetworkrdquo Journal of Uni-versity of Shanghai for Science and Technology vol 33 no 3pp 229ndash237 2011

[19] J-B Liu J Cao A Alofi A AL-Mazrooei and A ElaiwldquoApplications of laplacian spectra for n-prism networksrdquoNeurocomputing vol 198 pp 69ndash73 2016

[20] J D Luo Lecture Notes on Social Network Analysis SocialSciences Academic Press Beijing China 2nd edition 2010

[21] S Hayat S Wang and J-B Liu ldquoValency-based topologicaldescriptors of chemical networks and their applicationsrdquoApplied Mathematical Modelling vol 60 pp 164ndash178 2018

10 Mathematical Problems in Engineering