ATC full paper format-2014 Social Networks in Telecommunications Asoka Korale - Review

Annual Conference 2014 - IET- Sri Lanka

MODELING SCOCIAL NETWORKS IN MOBILE

TELECOMMUNICATIONS NETWORKS VIA

INFLUENCE DIFFUSIONAsoka Korale, Ph.D., MBA, CEng., MIET

Abstract: The identification of leaders and

communities of followers in Social Networks is

vital for implementing innovative business

strategies and marketing campaigns that can be

put in to effect by exploiting the hierarchical

relationships between individuals and their

consumption preferences.

This paper presents a novel approach for

analyzing the Social Network that arises as a

result of the hierarchical nature of communication

that occurs between the members of a particular

segment of the subscribers of a Mobile

Telecommunications Network. We identify leaders

and communities comprised of followers by

processing the way in which calls are initiated and

terminated between the subscribers. The call

pattern is translated in to a call graph using the

inherent properties of the interactions between

individual subscribers of the mobile network and

appropriately represented in an Adjacency matrix.

A community detection algorithm [2] is then

employed to identify those individuals with

significant influence in the network. The leaders

so identified are also validated using existing

notions about what constitutes a leader of a

subscriber segment in the context of a Mobile

Telecommunication Network.

Results from subscribers belonging to a Corporate

Telecommunications Network so analyzed are

presented identifying the leaders and the

communities formed around them. The

connectivity properties of the identified leaders are

then evaluated using existing methods to validate

the results of the new approach. A significant

innovation of this approach is the estimation of the

degree of membership of a given individual in a

particular community made possible by employing

this influence diffusion technique [2]. This leads

to the discovery of overlapping communities

populated by individuals who may display different

degrees of membership in more than one

community at a given time.

Business strategies a mobile network operator may

deploy by exploiting the underlying social network

discovered by this modeling to enhance revenues

through product promotions, advertisement

diffusion, churn reduction, and recommender

systems are also presented.

1. INTRODUCTION

It is often the case that networks exhibit hierarchical properties and the analysis of such networks to identify those nodes which lie at the root of the hierarchy is important for many scientific and business applications. It also the case that many of these networks exhibit modularity properties where the network may display natural partitions or clustering of nodes which can be described and understood as a process of community formation. Thus under these conditions it would be possible to partition the network so as to isolate the different communities with the aim of identifying groups of


nodes that belong to each of the community. This partitioning is usually done in a way that the there is a high density of links between members of a particular community while the links between communities are minimized.

Graph partitioning [6] and Spectral partitioning [7, 8] are the main techniques currently used for dividing networks in to clusters or groups. Graph partitioning algorithms however require as input the number of partitions that need to be created and thus do not automatically determine the optimum way of segmenting a network.

Thus the partitions so estimated have analogies to communities in social networks and the communities are usually headed by a leaders that are often the nodes near the root of the hierarchy. In this way one is able to identify communities made up of followers and leaders who have high importance or influence.

In this paper we examine several methods for modeling the Social Networks arising in Mobile Telecommunications Networks by modeling the mobile phone call pattern between subscribers. We present results for a novel method for the analysis of such Social Networks through the use an algorithm [2] that displays superior performance to the existing techniques employing modularity function [3, 4], graph and spectral partitioning. This algorithm performs automatic community detection and does not suffer from the drawbacks of the modularity approach related to resolution limit which may give results that may not be in line with the most intuitive partition of the network [5].

The algorithm also presents a method for estimating the degree to which a node belongs to a particular community by a membership vector with elements associated with each detected community. In this way it is possible to identify not only leaders of a particular community but also their respective followers who comprise the members of the community. A novel feature is then the detection of nodes that belong to more than one community to a certain degree at a given time as expressed by the membership function. Thus we are also able to identify nodes or individuals that act as bridges between communities.

2. SOCIAL NETWORK ANALYSIS

Social Network Analysis (SNA) is derived from the study of the interactions between individuals and

groups and has its origins in the science of Sociology, Sociometry and Psychology. In the graphical representation of such a social network the nodes are referred to as actors and the edges which represent the interactions between the nodes as ties or links.

While there is not much ambiguity in the definition of the nodes in social networks the definition of the edges however depends on the particular type of problem being studied. As such the physical meanings of the edges can be taken to signify friendships between individuals, professional relationships as found within certain organizations for instance, communication patterns between individuals in certain situations and even the exchange of goods/money.

Other representations of social networks take the form of “Affiliation Networks” (also referred to as Bipartite graphs) where two types of vertices are present with the links between the vertices indicating membership of an individual in a particular event / group.

An ego centric network on the other hand is the study of the network surrounding a particular individual, and thus does not encompass the entire social network or depict the connections between all actors. This is suitable when the network is very large comprising of a vast number of nodes and the aim is to picture the immediate neighborhood of the ego or the individual under study and those around it known in the literature as alters. 3. MODELING THE SOCIAL NETWORK

ARISING BETWEEN SUBSCRIBERS OF A

MOBILE TELECOMMUNICATION

NETWORK

The interactions between subscribers in a Mobile Telecommunications Networks can be modeled as a social network by utilizing the calling patterns between the individual subscribers to construct a “call graph” or a network of connections between subscribers. The nodes in the graph are then the subscribers or MSISDNs (Mobile Numbers representing the subscribers) and the links are indicative of calls between the nodes.

We believe that in such a scheme an edge can be established between two nodes if there has been a call between the respective MSISDNs. Often it is the case that an edge is established between two


nodes only if there has been a reciprocal call (i.e. both MSISDNs have called one another). This is to eliminate spurious links that may be formed by external agents and weak and “unimportant” relationships between subscribers. In such a scheme the call graph may be a simple unweighted and undirected one where a link is only established between nodes that have made a reciprocal call or exchanged a Short Message Service (SMS) message between them. In other configurations the graph may be a directed with the direction of the link indicating the direction of the originating call or SMS.

Unweighted call graphs of the nature described above don’t account for the strength of the relationship as expressed by the tie strength between two nodes. The model can account for this aspect by assigning a weight to each edge depending on the number of calls exchanged between two nodes or on the total amount of call time (minutes of use) between the subscribers. The total rupee value of the calls between two nodes can also considered in determining the tie strength, noting that this is a variable that may change with the time of day and day of week in markets that have differentiated pricing depending on the time the call is made.

There is greater importance attached to incoming calls as opposed to those outgoing in the social networks of telecommunications. This follows from an analogy taken from the World Wide Web, where the importance of a web page is dependent on the number of other web pages pointing to it. Thus web pages that have many links to it are considered of a higher rank than those that merely have many links pointing to other pages. The Google page rank algorithm utilizes this criterion and is based on the premise that while one can create a page with a large number of links to other pages it is the number of references by other pages to the web page in question that is indicative of its importance and should determine its place in the network hierarchy [10].

Considering the above inferences and arguments, in the analysis presented in this paper we modeled the Social Network of connections between the subscribers of the Mobile Telecommunications Network as a weighted undirected graph where a connection is established between two subscribers only if there are calls of a certain minimum duration and if there is at least one call in the reverse direction between the subscribers.

4. MATHEMATICS OF NETWORK ANALYSIS [1]Network theory is a vast discipline and only the most important details necessary for identification of leaders and community detection are presented here. The adjacency Matrix is a common mathematical representation of a network and in the case of a directed graph takes the form below. When the edges are weighted the value of the weight will apply to the corresponding matrix entry instead of unityAij=1 , if there is an edge from j to i

Aij=0 , otherwise

Centrality is a family of measures that seek to quantify the importance of a particular node in a network. As such there are many such centrality measures of which Degree centrality, Katz centrality, Page Rank and Eigen vector centrality are perhaps most encountered. Katz and Page Rank are closely related to and is a variant of the Eigen Vector centrality used in this paper.

Eigen Vector centrality is based on the premise that a node’s importance lies not only in the number of connections it has but also on the connections of its neighbors. So a node’s importance is measured by the number of connections it has and this is increased by having connections to other nodes that are also important. Eigen vector centrality thus assigns a score to each node that is the sum of the scores of its neighbors, and mathematically this is expressed as

x i'=∑

jA ij x j

, and when expressed as a vectorx (n)=Ax (n−1)which implies that by iterating

x (n)=An x (0 )

It can be shown that in the limit for large n, x approaches the principal Eigen vector of A (corresponding to the largest Eigen value). An important observation is that the Eigen values and Eigen vectors of a matrix provide global information about its structure. Thus the elements of the principal Eigen vector also provide an indication of the importance of each corresponding node.

Influence Diffusion, Spectral Clustering and Spectral Graph Partitioning are a few of the many techniques available for community detection. Figure 2, depicts the results for the Spectral Graph


Partitioning of the “Highland Tribes” test network depicted in Figure 1, obtained by thresholding the Eigen vector corresponding to the second smallest Eigen value of the Laplacian matrix.

Figure 1: Highland Tribes Social Network

The Laplacian L, is defined as L=D−A where D is a diagonal matrix composed of the sum of the corresponding columns of the Adjacency matrix

Di=∑i

A ij.

Figure 2: Detected Communities

The three communities and two components of the social network are partitioned via the thresholds, Figure 2. Degree centrality measures the number of incoming and outgoing connections at a particular node and is a powerful measure of the importance of a node.

In-Degree Dini=∑

jA ij

Out-Degree Dout i=∑

iA ij

5. ALGORITHM FOR LEADER IDENTIFICATION AND COMMUNITY DETECTION [2]

The algorithm implemented in the following analysis is based on that which was derived by Smilkov etal [2] and only the most salient points are reproduced here.

An influence matrix A' is defined using the

adjacency matrix A as

A ji

' =A ji+∑k

C jik

where C jik =min {Aki , A jk}the

transitive link weight from node i to j and its defined only for neighboring nodes.

To determine the overall influence at a node x i¿

the average influence of its neighbors are calculated via an iterative procedure

x ( t+1 )=T x ( t ) where

T ij=A ij

'

∑k

Akj'

The identification of leaders is via the set of neighbors with the largest influence on node i. The

neighborhood is defined Γ i={ j|T ji=maxk T ki}

and that node is denoted a leader if T ij⋅x i>T ji⋅x j

for all j∈Γ i .

A significant innovation introduced by this algorithm is the calculation of a membership function that allows fuzzy boundaries between communities, where one actor can belong to more than one community to a different degree. Thus each node has a membership vector where its elements sum to one, each element indicating the degree of membership of that node in a particular community.

Considering consensus dynamics the membership vector is determined via

y i( t +1)= 1∑

jA ji

∑j

A ji y j( t )

, at each iteration a weighted average membership figure is calculated.

Thus each node will have a membership vector giving its degree of participation in each community where the sum of this vector is unity. 6. RESULTS FROM A CORPORATE TELECOMMUNICATION NETWORK TO VALIDATE TECHNIQUEA well defined network of subscribers chosen from a corporate network was chosen to illustrate and


validate the technique for community detection, identifying leaders and their degree of membership in a particular community. It is shown that the leaders so identified belong almost exclusively to a single community and their followers exhibit a high degree of membership in their leader’s community while they may also have a lower degree of involvement in other communities.

The In-Degree is a commonly used and direct measure of the importance of a particular node (subscriber) or actor in this type of communication network with high degree measure indicating a greater level of importance bestowed upon that node. In the following analysis this In-Degree measure is used to validate those individuals identified as leaders by demonstrating that they indeed display a high value when compared with the other subscribers in the network.

The Adjacency matrix for the calls between the members of the corporate mobile network was constructed in such a way that only reciprocated calls of total duration greater than 6 minutes for all calls over the period were considered in establishing a link between two nodes (subscribers). The network was modeled as a weighted undirected graph with link weight taken to be the total amount of minutes of use between a particular pair of nodes.

The initial call records contained approximately 4000 incoming and outgoing calls between members of the mobile network having 55 members captured over a period of one week. The data was parsed to meet the above eligibility criteria as it is believed that meaningful relations exist between members that have reasonably long calls and also only when there is at least one call in the reverse direction that meets the total cumulative minimum duration criteria. Thus the link weight was taken to be the sum of the total number of incoming and outgoing minutes between two subscribers (nodes).

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MSIDN or Cx No

Deg

ree

of M

embe

rshi

p in

a C

omm

unity

Degree of Membership in Communities

Community 1Community 2Community 3Community 4

Figure 3: Degree of Membership

The degree of membership result (Figure 3) indicates that most nodes in this analysis mostly belong to one community and that the overlap of communities is not so prevalent. A less stringent requirement for the data parsing condition it was observed resulted in a greater number of nodes that exhibited greater overlap between several communities. Thus when a link is established between nodes for lower cumulative call duration than the six minutes chosen, a greater degree of overlap between communities was observed. Hence this parameter is one that can tune the degree of overlap by indirectly selecting the strength of the relationship between a pair of subscribers.

0 5 10 15 20 25 30 35 40 45 50 55

1

2

3

4

5Communities

Leader Community Size 3 92336

39 9 3 4

MSISDN or Cx No

Com

mun

ity ID

Figure 4: Communities and Leaders

Figure 4, presents the leaders (nodes 3, 9, 23 and 36) and the corresponding number of followers given by community size in their respective communities. The red hatches indicate those nodes that have not attached to a particular community or leader, but are counted as part of community 1, for sake of presentation. Figure 4, also indicates that leaders with node numbers 3, 9, 23, and 36 belongs to the communities 1, 2, 3 and 4 respectively.

It is also observed that the leaders (nodes) so identified belong exclusively to one community by having a membership value of unity (Figure 3). Thus nodes 3, 9, 23, and 36 belong only to one community and are not members of any other community even to a lower degree. This also validates their leadership position in the network. It also is observed that there are a few nodes that have membership values less than unity thus belonging simultaneously to more than one community. It is also observed that this degree of participation is clustered mainly at the lower and upper regions of the graph indicating that those nodes that have


multiple memberships still strongly associate with one cluster (community) than the other.

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

9In Degree

MSIDN or Cx No

Deg

ree

Figure 5: In-Degree at each node

Figure 5 depicts the In-Degree measure of each of the nodes in the network participating in the respective communities. There is strong correlation between In-Degree and selection of a node as a leader. Thus it is observed that nodes 3, 9, 23 and 36 do indeed exhibit a high In-Degree relative to the other subscribers which is commensurate with their elevation to the status of leader of a community. In- Degree alone however does not make a leader as it’s the connectivity of the neighboring nodes that ultimately counts. There are a number of nodes with zero In-Degree that are the result of the original filtering to obtain only those relationships that are meaningful and eliminate spurious links. Thus we are able to validate the results of the Social Network modeling of the Mobile Telecommunication Network via the influence diffusion analysis technique by utilizing the more traditional approach of In-Degree. 7.0 BUSINESS AND MARKET STRATEGIES FOR NETWORK OPERATORS Increasingly businesses are aware of the value of the “buzz” created by campaigns and watch social media for signs of chatter that can help predict the success or failure of a new product or initiative. Social media then is an indicator as well as a method for spreading the word or a particular message across its communities. The ability to identify those individuals within the network with “social power” is key to implementing these strategies.

The identification of corporate leaders such as senior managers and CEOs for inclusion in ones customer base is a less subtle form of the same strategy that has the benefit of attracting those subordinate connections from a particular institution

and is a well practiced approach. Thus diffusing an advertisement, product idea or message across the customer base and then to the wider public is more efficiently done by targeting the message to these key individuals in the social hierarchy in a network. In this way the message is more likely to filter to the larger communities lead by the “influential” individuals. This is far more efficient and cost effective than a blanket advertizing campaign or broadcasting the message to a random sample of the base.

The increasing synergies that arise due to the convergence between the mobile telecommunications and the internet worlds give a promoter the opportunity of spreading a message between the two environments. Thus internet products may be advertized through mobile and vice versa. Additionally the social networks arising from social media such as Facebook and Twitter can readily be exploited by the social networks in telecommunications networks provided care is taken to match the “interest profile” of a potential customer. In general those individuals that form social networks do have many commonalities that can take the form of common interests, demographics, and lineage among other attributes. Thus it may be construed that a mobile user who accesses the internet and browsers news sites may be a candidate for a subscription to a certain type of online news magazine.

Further, the analysis of the attributes of the members of a particular community formed around a leader may lead to the discovery of common traits that can exploited by a shrewd marketer. Thus the identification of a leader of a community combined with the knowledge of some overall characteristics of the followers will enable the creation of a well tailored message targeting the leader but aimed to be also appealing to the followers of that segment and the community at large.

Sentiment analysis of twitter feeds and postings on social media plays an increasingly larger role in a company’s communications strategy providing almost immediate feedback on an organization’s initiatives and corporate image. As influencing the opinions of existing and potential new customers is important to the success of a business in the internet age, the corporate image usually built on fundamentals such as service quality, customer service and reliability benefits from managing and influencing the conversations taking place on social media. In this regard well designed messages


directed to “influential” individuals in the social hierarchy can help burnish a company’s image, create awareness and push products, raising the profile of a company.

Product bundling and opportunities for cross sell and up sell are all made more effective through the utilization of social networks, so much so that social media marketing is a vital part of many innovative organizations. These promotional initiatives can be considered as being the result of a chain process and when triggered by individuals with influence and social power can have the effect of rippling through the network triggering other individuals to perform similar actions. Churn events is a prime example of this phenomena where the loss of an important customer can result in the loss of a whole host of other “followers” [9]. Thus the retention of key individuals in the network hierarchy is crucial to a business as it lowers churn rates, reduces negative vibes and rationalizes customer acquisition costs. Additionally segmentation of the customer base and can also be made more effective when based on communities combined with other profiling attributes of interest. Product and service recommendations derived from Recommender systems are a very common part of the internet experience. Essentially the recommender algorithm determines the combinations of services and products a customer has purchased and makes a recommendation on a product not already in the portfolio of the consumer based on the consumption pattern of products of other customers who have a very similar profile to the customer. This profile will take in to account a number of attributes such as demographics, income and spending, and product preferences. Social networks enhance this process as recommendations from friends and those with social influence go further than mere advertisements or ratings. Thus for example a hotel / service recommendation from a friend, colleague or someone with influence will make a significant difference in influencing a choice than a mere banner / pop up advertisement or ratings service [11].

Finally, the single view of the customer envisaged by business to arrive at a complete understanding of the needs and worth of a customer will also depend on that person’s position in the social hierarchy. As examined earlier, the importance of a customer or subscriber cannot be determined solely on revenue contributions but also should take in to account that

person’s position in the social network, which is a measure of the ability to act as an attractor for other customers, products, services and the spread of influence.

8. CONCLUSIONThis paper presented a novel technique for the analysis of the Social Networks that arise in Mobile Telecommunications Networks. In this technique we modeled the call pattern between the subscribers of the mobile network as a weighted undirected graph using an influence diffusion algorithm to estimate the key actors and their properties in the network. Several schemes for modeling the mobile phone call patterns between the subscribers in the network as call graphs were studied and the impact on the resulting social network analyzed.

Leaders and followers of communities formed among the mobile subscribers of a corporate network were identified via this technique and validated using In-Degree measure. Their more significant attributes such as connectivity, centrality were also analyzed to understand the role they play in the communities. The degree of membership in a particular community was presented as a measure to determine those subscribers that may act as links between two or more communities of subscribers instead of merely belonging exclusively to one community and in that respect play an important role.

In conclusion the strategies a mobile operator should adopt to enhance its competitive position in the industry through the deeper understanding of the interactions and relationships of its key subscribers and the communities they represent were discussed. The modeling thus illustrates the significance, relevance and power of social network analysis in mobile telecommunications.

9. ACKNOWLEDGEMENTSN.S. Ekanayake, BSc. (Hons) for providing business intelligence and detailed call data records from a live corporate mobile telecommunication network.

10. REFERENCES[1] Newman, MEJ, Networks, Oxford University Press, 2013, pp 109-149.[2] D. Smilkov, A. Stanoev, L. Kocarev, Identifying communities by influence dynamics in social networks, Physical review E, 2011.[3] M. E. J Newman and M. Girvan. Physical Review E 69, (2004).


[4] A. Clauset, M. E. J. Newman and C. Moore. Finding community structure in very large networks. Phys. Rev. E 70, (2004).[5] B. H. Good, Y. A. Montjoye and A. Clauset, Performance of modularity maximization in practical contexts, Phys. Rev. E 81, (2010).[6] Kernighan, B. W. and Lin, S., An efficient heuristic procedure for portioning graphs, Bell System Journal, (2010). [7] Fiedler, M., algebraic connectivity of graphs, Czech. Math. J. 23, 298-305, (1973).[8] Pothen, A., Simon, H., and Liou, K-P., Partitioning sparse matrices with eigenvectors of graphs, SIAM J Matrix anal. Appl. 11, 430-452, (1990).

[9] Dasgupta, K., Singh, B., Social ties and their relevance to churn in mobile telcom networks, EBDT, (2008).[10] Brin, S., Page, L., The anatomy of a large scale hypertextual web search engine., Proceedings of 7th

International WWW Conference, (1998).[11] Mahajan, V., Muller, E., Bass, F., New product diffusion models in marketing: A review and directions for research., Journal of marketing, (1990).

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ATC full paper format-2014 Social Networks in Telecommunications Asoka Korale - Review