Cascading effects in interdependent networks

he past decade has witnessed a surge of interest incomplex networks, including electric grids, telecom-munication networks, transportation systems, socialnetworks, and biological networks. Many existing

studies are devoted to understanding the topological charac-teristics of networks, such as node-degree distribution, nodeclustering coefficient, network modularity, degree correlation,and giant components [1]. Since these topological propertiesare intimately related to the functionality of systems, a deepunderstanding of them provides key insights into practical sys-tems and guidance on how to design and optimize these sys-tems. Nevertheless, most of the existing studies on complexnetworks have focused on individual networks only. Modernsystems, however, rather than being isolated, are becomingincreasingly dependent upon and interacting with each other,and it is in this sense that we call these interacting networks“interdependent networks.” Needless to say, due to the inter-dependency and the interplay of the constituent systems, someinteresting and even surprising behaviors may take place.

Cyber-physical systems (CPS) [2, 3] are emerging as theunderpinning technology for major industries in the 21st cen-tury. A cyber-physical system is a system built on a tight com-bination of, and coordination between, physical elements (e.g.electric grids and transportation systems) and cyber networks,where cutting-edge communication and computation tech-nologies are integrated with a physical infrastructure networkin order to enhance the control and management of the physi-cal system. Observe that CPS are often built upon the func-tional interdependence between the cyber network and the

physical infrastructure network, in the sense that the function-ality of one network depends on that of the other (Fig. 1a).An archetypal example of such a CPS is smart (electric) grids,where the operation of the electric grids relies on the real-time control via the communication network, and further thelatter would not function without the power supply from theformer. In CPS, due to this functional interdependency, fail-ures occurring to nodes/links in one network can cause fail-ures to nodes in the other network. This, in turn, can causefailures to other nodes in the former network (where the ini-tial failures occurred). In this way, even a small fraction offailed nodes in one network may trigger cascading failures,that is, a recursive process of failures between two networks,eventually resulting in devastating damage to the entire sys-tem [2]. A real-world example of such cascading failures inCPS is the electrical blackout that affected much of Italy on28 September 2003, where a failure in one power station trig-gered a recursive process of failures between power stationsand communication servers connected to their geographicallynearest power station [2].

Another outstanding example of interdependent networksis coupled social networks. Recent advances of Internet andmobile communication technologies make it easier for peopleto connect with each other, through online social networkssuch as Facebook, Twitter, FriendFeed, and YouTube. Clear-ly, these online social networks are not completely isolated,since people can join several of the networks at the sametime. Rather, these networks are coupled through the multi-membership people, as illustrated in Fig. 1b, and in fact, themulti-membership people may facilitate information spread inthe social networks. For instance, when a multi-membershipperson receives a message from someone through Twitter, theperson can forward the message to his/her friends via Face-book. Thus, information spread in one network can facilitatethat in another network, and further may trigger an informa-

T

82 IEEE Network • July/August 2014

AbstractModern systems are increasingly dependent upon and interacting with each other,and become interdependent networks. These interdependent networks may exhibitsome interesting and even surprising behaviors due to the interdependency and theinterplay between the constituent systems. In this article we focus on two importantphenomena, namely cascading failure in cyber-physical systems (CPS) and informa-tion cascade in coupled social networks. Specifically, cascading failures may occurin CPS that exhibit functional interdependency between two constituent systems(e.g. smart grid); information cascade may happen in multiple social networks thatare coupled together by so-called multi-membership individuals. This articleexplores these two types of cascading effects in interdependent networks byreviewing existing studies in the literature. We review different models in the litera-ture to study the two types of cascading effects in interdependent networks, andhighlight the key findings from these studies.

Cascading Effects in Interdependent Networks

Dong-Hoon Shin, Dajun Qian, and Junshan Zhang

T

0890-8044/14/$25.00 © 2014 IEEE

The authors are with Arizona State University.

This research was supported in part by the U.S. DTRA grant HDTRA1-13-1-0029 and DoD MURI project no. FA9550-09-1-0643.

SHIN_LAYOUT_Layout 1 7/17/14 2:21 PM Page 82

tion cascade across multiple networks. Hence, theinformation propagation in one network is depen-dent upon that in other networks, and it is in thissense that we can view the (coupled) social net-works as interdependent networks.

The above two instances of interdependent net-works reveal two types of cascading effects ininterdependent networks, namely cascading failureand information cascade. In this article we explorethese two cascading effects in interdependent net-works. First, we examine the vulnerability of inde-pendent networks to cascading failures, whichhelps us to understand how to build a resilientinterdependent network against cascading failures.This is a major issue to be addressed in the robustdesign of CPS, especially the infrastructures criti-cal to the public (e.g. electricity, water, oil, andgas), since if a cascading failure occurs in a CPS,even with a small probability, it may result in acatastrophic disaster. Second, we investigate theinformation diffusion process across multiple over-lapping social networks, and characterize the pos-sible information epidemic. We aim to quantifywhen the coupling among social networks canfacilitate information diffusion dramatically, sothat certain important information, such as breaking news andemergency messages, can spread at an unprecedented speedthrough a large population.

We explore these two types of cascading effects in interde-pendent networks by reviewing some existing studies in the lit-erature. The existing studies summarized in this article arebased on the modeling of interdependent networks and theo-retical analysis of the cascading effects, which capitalizes main-ly on the theory of random graphs. The theory of randomgraphs is a powerful tool to analyze the behaviors of real-worldnetworks [1, 4, 5]. It offers an analytically tractable frameworkto characterize important topological properties of large-scalenetworks, including average diameter, node clustering coeffi-cient, network modularity, degree correlation, and phase-tran-sition behaviors of giant components [1]. Such topologicalproperties reflect different network functionalities under dif-ferent scenarios. Notably, the theory of random graphs hasbeen widely used to study single networks. The existing studiesintroduced in this article advance this line of study by applyingthis analytical tool to interdependent networks.

The rest of this article is organized as follows. In the fol-lowing two sections we review different models proposed inthe literature to study the two types of cascading effects ininterdependent networks — first cascading failures and theninformation cascade — and highlight the key findings fromthese studies. Finally, we present concluding remarks.

Cascading Failures in InterdependentNetworksIn this section we first discuss the vulnerability of interdepen-dent networks to cascading failures, and then address theissue of how to design robust interdependent networks againstcascading failures.

Vulnerability of Interdependent Networks toCascading FailuresThe vulnerability of interdependent networks to cascadingfailures was first studied in [2]. An interdependent networkconsisting of two networks, networks A and B, is modeled by

two random graphs1 with the same number of nodes. Nodeswithin each network are connected with each other by intra-edges, and pairs of nodes in the two different networks areconnected by bidirectional inter-edges. These bidirectionalinter-edges represent a one-to-one correspondence of func-tional interdependence between nodes in network A andnodes in network B (Fig. 2a). That is, a pair of nodes that areconnected by a bidirectional inter-edge provide functionallynecessary support to each other. For instance, in smart gridthe interdependency between a power node, nA, and a com-munication node, nB, can be represented by a bidirectionalinter-edge, meaning that nA relies on nB for its communica-tions with other power nodes, and also nB relies on nA for itspower supply. A node is regarded as functioning if the follow-ing two conditions are satisfied:• The node is connected to a functioning node in the other

network (by an inter-edge).• The node belongs to a functioning giant component2 within

its own network. A cascading failure is triggered by randomly choosing a

fraction 1 – p of nodes in one network that will fail. The dam-age incurred by a cascading failure is measured in terms ofthe size of a functioning giant component (i.e. a set of nodesthat still function) when the cascading failure ends; the small-er its size, the higher the damage. The size of a functioninggiant component is computed at each stage of the cascadingfailure by using the theory of random graphs until the cascad-ing failure ends.

One of the key findings in [2] is that interdependent net-works also exhibit a phase-transition behavior as single net-works. Specifically, this means that if the value of p is below acertain threshold pc, a cascading failure results in a completesystem failure; otherwise, there would still exist a functioninggiant component in both networks, even after the cascadingfailure. This suggests that the critical threshold, pc, can beused as a criteria to evaluate the system robustness; and a

IEEE Network • July/August 2014 83

Figure 1. Instances of interdependent networks: a) interdependencebetween the cyber network and the physical infrastructure network incyber-physical systems; b) coupling among (physical and online) socialnetworks due to multi-membership individuals.

Face-to-face friends

Network coupling

Multi-membership

Physical system(e.g. power grid)

Cyber network(e.g. Internet)

Support

(a) Interdependence between the cyber network and thephysical infrastructure in cyber-physical systems.

(b) Coupling among (physical and online) social networksdue to multi-membership individuals.

1 A random graph is a graph constructed by starting with a set of nodesand adding links between them randomly. Different random graph modelshave been proposed based on observations of real-world networks.


lower value of pc indicates that the system is more resilientagainst node failures. Furthermore, the numerical results in[2] show that interdependent networks have a larger value ofpc compared to that of each constituent network. This impliesthat the interdependent networks, as a whole, are more vul-nerable to cascading failures than each single network.

Since the one-to-one correspondence model used in [2] istoo restricted to capture more realistic scenarios in whicheach node in network A can be supported by more than onenode in network B and vice versa, a generalized interdepen-dence model has been proposed and studied in [7]. In thismodel each node supports and is also supported by a randomnumber of nodes in the other network. In contrast to the one-to-one correspondence model in [2], each node may havemultiple supports and thus be able to function as long as it issupported by at least one node in the other network. More-over, the inter-edges are unidirectional, that is, nodes may notsupport each other (Fig. 2b, where v1 supports v1′ but not viceversa). Under this generalized model, the numerical results in

[7] show that the system becomes more resilient against cas-cading failures as the average number of inter-edges per nodeincreases.

Robustness of Interdependent Networks againstCascading FailuresThe numerical results in [7] shed light on a crucial role ofinter-edges with respect to the robustness of interdependentnetworks. That is, inter-edges can be viewed as “resources” tocombat cascading failures. This, in turn, implies that howthese resources are allocated, that is, the way in which theinter-edges connect the constituent networks, may greatlyimpact the propagation of cascading failures, thus on therobustness of the overall system. With these observations, anatural question arises: given a budget on the amount ofavailable resources, that is, the average number of inter-edgesper node, how to optimally allocate inter-edges so as toenhance the robustness of the overall system?

Case 1: Topology of Each Constituent Network is Unknown —This question has been addressed in [8], assuming that theintra-edge topologies are unknown, by answering the follow-ing two questions:• Which strategy, between random allocation and regular

allocation (that allots exactly the same number of inter-edges to every node), should be used to determine thenumber of inter-edges supporting each node?

• Which type of inter-edges, being unidirectional or bidirec-tional, should be allocated to mitigate the propagation ofcascading failures?

Random Allocation versus Regular Allocation — It is shownin [8] that the regular allocation always leads to a morerobust system than the random allocation (i.e. the allocationin [7]). We can understand this result from the followingintuitive explanations (refer to [8] for a rigorous proof). Therandom allocation may yield nodes that have no inter-edgeand consequently do not function even before a cascadingfailure occurs, whereas the regular allocation guaranteesthat every node in both networks always has at least oneinter-edge. Furthermore, without the knowledge of theintra-edge topologies, it is difficult to tell which nodes playa more central role in preserving the connectivity of theconstituent networks. Hence, in order to combat randomfailures, it is reasonable to treat all nodes as being equallyimportant and give them the same priority in the inter-edgeallocation.

Unidirectional Inter-Edge versus Bidirectional Inter-Edge — It isshown in [8] that cascading failures are easier to propagate inthe interdependent networks with unidirectional inter-edgesthan in those with bidirectional inter-edges, where the numberof unidirectional edges is given twice the number of bidirec-tional edges, for a fair comparison. This result can be under-stood with the illustrative example in Fig. 2 (refer to [8] for arigorous proof). Suppose that the nodes v1 and v2 stop func-tioning due to a failure. In the case of using bidirectionalinter-edges, since v1′ and v2′ are supported by and also sup-

IEEE Network • July/August 201484

Figure 2. Instances of the two types of inter-edges: a) bidirec-tional inter-edges; b) unidirectional inter-edges.

(a) Bidirectional inter-edges.

(b) Unidirectional inter-edges.

v1 v’1

v2 v’2

v1 v’1

v3

v2 v’2

v4

2 A giant component is a connected component that contains a constant fraction of nodes in a graph. It represents different physical meanings under dif-ferent scenarios. For example, a giant component represents a fraction of nodes that can still function after external attacks [6], or a collection of influ-enced individuals in an epidemic [4–6]. In random graph models, a variety of issues, such as network stability and spread of epidemics, can be understoodby studying giant components. The percolation theory [4–6] states that giant components in random graphs exhibit a phase-transition behavior related tonetwork connectivity. That is, if the network is densely connected above a critical threshold, it is highly likely that a giant component would still exist in thenetwork; otherwise, there would exist no giant component in the network.


port v1 and v2, which have already failed, the failures of v1 andv2 propagate only to v1′ and v2′. On the other hand, in thecase of using unidirectional inter-edges, the failures of v1 andv2 propagate further to v3 and v4 since v1′ and v2′ supportother functioning nodes, v3 and v4.

These results reveal that if the intra-edge topologies areunknown, the regular allocation of bidirectional inter-edges(i.e. allotting exactly the same number of bidirectionalinter-edges to all nodes) is the optimal inter-edge alloca-tion strategy. As an example, Fig. 3 illustrates the regularallocation strategy with two bidirectional inter-edges toevery node, and also depicts how a cascading failure propa-gates across the two constituent networks. In addition, for acomparison of the four possible inter-edge allocationstrategies — the random allocation of unidirectional orbidirectional inter-edges and the regular allocation of uni-directional or bidirectional inter-edges — in terms ofrobustness, Fig. 4 shows how the critical threshold, pc, forthe four strategies varies as the average number (k) ofinter-edges increases. Here the two networks are modeledby Erdös-Rényi (ER)3 graph with the same average degreeof inter-edges. It is observed that the regular allocation ofbidirectional inter-edges yields the lowest value of pcamong the four strategies. This confirms that the regularallocation of bidirectional inter-edges achieves the highestresilience against cascading failures.

Case 2: Topology of Each Constituent Network is Known —Many real-world infrastructure networks (e.g. smart grid) arenot randomly deployed. But rather, they are carefully designedwith certain topological structures to achieve their functionaland performance objectives. Inspired by this observation, in[9] a theoretical framework has been presented to study thestructural robustness of interdependent networks when theintra-edge topologies are known. This framework uses a“geometry of networks” approach to the network robustness.Specifically, in order to quantify the roles of nodes in a net-work, a key metric, the so called structural centrality, is mea-sured by using the (Moore-Penrose) pseudo-inverse of thegraph Laplacians (L+). Based on the topological interpreta-tion of L+ with respect to the bi-partitions of a graph (net-work) [10], the structural centrality and the roles of individual(coupled and uncoupled) nodes in interdependent networksas well as the robustness of interdependent networks as awhole are measured.

Using this framework, it is studied in [9] how the way in

which pairs of nodes in two networks are coupled or gluedtogether (thereby introducing interdependence) affects therobustness of the resulting interdependent networks. With afew examples (i.e. two types of tree networks — stars andchains — and the Italian power grid network), it provides acomparative study for three different gluing strategies basedon the structural centralities of nodes: high-high, low-low, andrandom. The results show that among the three strategies, thelow-low strategy yields more robust coupled/glued networks asthe number of coupled pairs increases. This indicates that dif-fusing and distributing interdependencies among a large num-ber of (geographically dispersed) node-pairs in the twoconstituent networks is likely to produce more robust interde-pendent networks.


Figure 3. An illustration of a cascading failure occurred in two interdependent networks constructed by theregular allocation of bidirectional inter-edges. Networks A and B consist of nodes {v1, v2, … , v6} and nodes{v1′, v2′, … , v6′}, respectively, and every node has two bidirectional inter-edges. A cascading failure is trig-gered by a failure of nodes v1 and v2. In Stage 1, v1 and v2 are removed from the system along with their(inter- and intra-) edges. As a result, v3 fails since it becomes disconnected from the functioning giant com-ponent in network A. The failure of v1, v2, and v3 makes v2′ and v3′ have no support and consequently fail.In Stage 2, the consequence of the removal of v2′ and v3′ from network B is shown: nodes v1′ and v6′ failsince they are disconnected from the functioning giant component in network B. In Stage 3, v6 fails since ithas no support due to the failure of v1′ and v6′. After v6 is removed, the cascading failure stops. The remain-ing functioning nodes are {v4, v5, v4′, v5′}.

Stage 3

v6

v5 v’5

v4 v’4

Stage 2

v6 v’6

v’1

v5 v’5

v4 v’4

Stage 1

v6 v’6

v3

v5 v’5

v4 v’4

v’3

v’2

v’1

Initial set-up

v6 v’6

v3

v2

v1

v5 v’5

v4 v’4

v’3

v’2

v’1

Figure 4. A comparison of the four inter-edge allocationstrategies. A lower value of pc indicates higher systemrobustness.

k32

0.3

0.2

Pc

0.4

0.5

0.6

0.7

0.8

4 5 6 7 8 9 10

Unidirectional and randomUnidirectional and regularBidirectional and randomBidirectional and regular

3 Erdös-Rényi (ER) model is an important type of random graphs. Itassumes that each pair of nodes are randomly connected with the sameprobability, and as a result each node has a Poisson degree distribution[1].


Information Cascade in InterdependentNetworksIn this section we turn our attention to an overlaying social-physical network model to study the information cascade insocial networks that are coupled together. We also provide acase study to illustrate the diffusion of real-time information.

Information Diffusion in Overlaying Social-PhysicalNetworksAn overlaying social-physical network model to study theinformation cascade across multiple social networks has beenproposed in [11]. This model consists of two networks, a phys-ical information network W and an online social network F, asshown in Fig. 5a. Here, the nodes in W and F represent a per-son and an online user, respectively. Each network is modeledas a random graph with an arbitrary degree distribution, andeach person joins the online social network, F, with probabili-ty a. Intra-edges within W and F represent face-to-face inter-actions and online communications, respectively. Inter-edges(denoted as red dotted links in Fig. 5a) connect a person in Wand an online user in F, indicating that the identity of theonline user in F is the person in W. The considered scenario isthat a piece of information starts to spread from a single nodeand then propagates to other nodes through both face-to-faceinteractions and online connections.

Using this model, the following two questions are posed tocharacterize the information epidemic: • What is the critical threshold for an information epidemic

to happen?• What is the expected size of the information epidemic, if it

happens?Since the set of nodes that receive a message forms a connect-ed component including the source node (that originates themessage), the information epidemic can be characterized bystudying the phase-transition behavior of a giant component.In light of this interpretation, the above two questions can berecast as the following:• What is a condition under which a giant component exists?• What would be the size of the giant component, if it exists?

A major challenge in studying the behavior of a giant com-ponent in the overlaying social-physical network model comesfrom its interdependence structure. To resolve this issue, theoverlaying social-physical network is transformed into anequivalent single network, as shown in Fig. 5b, where eachnode in W and its corresponding online member in F aremerged into a single node. As a result, the new graph becomes

an inhomogeneous random graph, where nodes are connectedby two types of edges, that is, the face-to-face and the onlineconnections. With this new graph the size of a giant compo-nent can be quantified by capitalizing the results in [12].

The numerical results in [11] reveal that conjoining thephysical information network with the online social networkcan facilitate information diffusion dramatically. In particular,an interesting finding is that even if no information epidemichappens in each individual network alone, an information epi-demic can take place in the conjoined social-physical network.To quantify, consider the physical information network W andthe online social network F that are ER graphs with the aver-age degree λw and λf, respectively. In Table 1 we presentsome numerical comparisons on message propagation in dis-joint and coupled social-physical networks. If two networksare disjoint, in order for a giant component to exist in eachnetwork, it would be required that λw > 1 and λf > 1 [4].However, if the two networks are coupled with a = 0.1 (i.e.when 0.1 fraction of persons in the physical network W jointhe online social network F), it suffices to have λf = λw = 0.76in order for an information epidemic to happen [11]. Further-more, conjoining the two networks can significantly increasethe fraction of persons who receive the information. Forinstance, in a single ER network W with λf = 1.5, a piece ofinformation originated from an arbitrary person can reach atmost 58 percent of the population. On the other hand, if thesame network W is conjoined with an ER network F with a = 0.5and λf = 1.5, up to 82 percent of the population can be influ-enced [11].

Case Study: Diffusion of Real-Time InformationReal-time information is effective only for a limited timeduration and thus needs to be delivered before it expires. Forinstance, once a time-limited coupon is released from a ser-vice provider (e.g. Groupon or Dealsea.com), people can

IEEE Network • July/August 201486

Figure 5. Overlaying social-physical network models: a) an overlaying social-physical network; b) inhomogeneous network corre-sponding to the above overlaying social-physical network with two types of edges: blue and green edges representing the onlineand the face-to-face connections, respectively; c) an overlaying social-physical network with cliques.

IndividualOnline user

Face-to-face linkOnline linkConnection betweenindividual and onlinemembership

Online social network

Physical information network

Online social network

Physical information network

(a) An overlaying social-physical network.

(b) Inhomogeneous network correspondingto the overlaying social-physical shown in (a)

with two types of edges: blue and greenrepresenting the online and the

face-to-face connections, respectively.

(c) An overlaying social-physical networkwith cliques.

a

b d

IndividualOnline userIntra-clique link

Inter-clique linkOnline linkCliqueConnection betweenindividual and onlinemembership

c

Table 1. Numerical comparisons on message propagation indisjoint and coupled social-physical networks.

Disjointed Coupled

Average degrees requiredfor information epidemic

λw > 1 andλf > 1

λw ≥ 0.76 and λf ≥ 0.76

Percentage of populationinfluenced by informationepidemic

58% 82%


share this news by either talking to friends or posting it onFacebook. If the coupon expires, however, it would no longerbe useful. This means that the influence of real-time informa-tion is affected by the speed of the information spread; thefaster the information passes from one to another, the morethe people can timely learn the information. When only theface-to-face communications are used, real-time informationwould be much more difficult to spread before its expiry ifpeople are far away from each other. Hence, the diffusion ofreal-time information in physical information networks hingesheavily on the physical distances between people.

The recent work [13] has explored in-person interactionsover the population. Its finding indicates that the physicalinformation network can be modeled as a social graph madeup of a large number of small cliques, each representing agroup of people who are close to each other. Within a clique,messages can spread quickly via frequent face-to-face interac-tions. However, across the cliques that are far away, it takeslonger time for messages to spread. Thus, the real-time infor-mation is less likely to spread across cliques via face-to-facecontacts before it expires.

Inspired by this finding, a model of overlaying a social-physical network with a clique structure has been proposed in[14] (Fig. 5c). In this model the physical information networkconsists of many cliques, and the size of cliques follows a cer-tain distribution. The persons in the same cliques are fullyconnected, indicating that information can quickly spreadwithin a clique. In this model the techniques used in priorworks cannot be directly applied due to the clique structure.To handle the clique structure, the proposed model is trans-formed into an equivalent single network so that the diffusionof real-time information can be characterized in terms of thesize of a giant component by using the theory of inhomoge-neous random graphs. The numerical results in [14] revealthat real-time information could be much easier to propagatein a social network when cliques of a large size exist.

Concluding RemarksIn this article we presented an overview of the two types ofcascading effects in interdependent networks, namely cascad-ing failure and information cascade. Since conjoined interde-pendent networks can be more vulnerable to cascadingfailures, we explored the issue of how to design interdepen-dent networks so as to make the resulting system more robustagainst cascading failures. Next we showed that couplingamong social networks can facilitate information diffusiondramatically.

We believe that the studies on interdependent networksintroduced in this article scratch only the tip of the iceberg.As the area of interdependent networks is an emerging field,there are many questions to be addressed along and beyondthe line of research presented in this article. For instance, it isnatural to ask the following questions: How can we apply thegained insights and results to practical systems, such as thedesign of robust smart grid and the prediction of informationspread in social networks for specific types of information, orwith certain social-networking structures? What are otherimportant characteristics/behaviors that interdependent net-

works would have? Can we build more practical models tocapture the unique characteristics (e.g. functional roles andimportance of nodes) of real-world interdependent networks(e.g. smart grid)?

References[1] R. Albert and A. L. Barabsi, “Statistical Mechanics of Complex Networks,”

Reviews of Modern Physics, vol. 74, no. 1, 2002, pp. 47–97.[2] S. V. Buldyrev et al., “Catastrophic Cascade of Failures in Interdependent

Networks,” Nature, vol. 464, 2010, pp. 1025–28.[3] CPS Steering Group, Cyber-Physical Systems Executive Summary, 2008.[4] M. E. J. Newman, S. H. Strogatz, and D. J. Watts, “Random Graphs with

Arbitrary Degree Distributions and Their Applications,” Physical Review E,vol. 64, no. 2, 2001.

[5] M. E. J. Newman, “Spread of Epidemic Disease on Networks,” PhysicalReview E, vol. 66, no. 1, 2002.

[6] R. Albert, H. Jeong, and A. L. Barabsi, “Attack and Error Tolerance ofComplex Networks,” Nature, vol. 406, no. 6794, 2000, pp. 378–82.

[7] J. Shao et al., “Cascade of Failures in Coupled Network Systems withMultiple Support-Dependent Relations,” Physical Review E, vol. 83, no.036116), 2011.

[8] O. Yagan et al., “Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures, and Robustness,”IEEE Trans. Parallel Distrib. Syst., vol. 23, no. 9, 2012, pp. 1708–20.

[9] G. Ranjan and Z.-L. Zhang, “How to Glue a Robust Smart-Grid? A Finite-Network Theory for Interdependent Network Robustness,” Proc. SeventhAnnual Wkshp Cyber Security and Information Intelligence Research (CSI-IRW11), 2011.

[10] G. Ranjan and Z.-L. Zhang, “Geometry of Complex Networks and Topo-logical Centrality,” Physica A: Statistical Mechanics and its Applications,vol. 392, Elsevier, May 18, 2013, pp. 3833–45.

[11] O. Yagan et al., “Information Diffusion in Overlaying Social-Physical Net-works,” Proc. 46th Annual Conf. Information Sciences and Systems,2012.

[12] B. Sderberg, “General Formalism for Inhomogeneous Random Graphs,”Physical Review E, vol. 66, no. 066121, 2002.

[13] K. Zhao et al., “Social Network Dynamics of Face-to-Face Interactions,”Physical Review E, vol. 83, no. 5, p. 056109, 2011.

[14] D. Qian et al., “Diffusion of Real-Time Information in Social-Physical Net-works,” Proc. IEEE Globecom, 2012.

BiographiesDONG-HOON SHIN ([email protected]) is an Assistant Research Profes-sor at Arizona State University, Tempe, Arizona, where he was a PostdoctoralScholar from Aug. 2012 to Aug. 2013. He received his B.E. degree fromKorea University, Seoul, Korea, in 2003, his M.S. degree from KoreaAdvanced Institute of Science and Technology (KAIST), Daejeon, Korea, in2006, and his Ph.D. degree from Purdue University, West Lafayette, Indiana,in 2012. He was a graduate intern at Intel’s Wireless Standards andAdvanced Technologies Group from Aug. 2011 to Jun. 2012. His researchinterests span the areas of communication, cyber-physical and social networks,with an emphasis on the security and privacy of these networks.

DAJUN QIAN ([email protected]) received his Ph.D. degree from the Departmentof Electrical, Computer and Energy Engineering at Arizona State University in2012. Before that he received his B.S. and M.S. degrees of Electrical Engi-neering from Southeast University, Nanjing, China, in 2006 and 2008,respectively. His research interests include wireless communications, social net-works, and cyber-physical systems.

JUNSHAN ZHANG ([email protected]) received his Ph.D. degree from theSchool of ECE at Purdue University in 2000. He joined the School of ECEE atArizona State University in August 2000, where he has been a Professorsince 2010. His interests include cyber-physical systems, communications net-works, and network science. His current research focuses on fundamentalproblems in information networks and energy networks, including modelingand optimization for smart grid, network optimization/control, mobile socialnetworks, crowdsourcing, cognitive radio, and network information theory. Heis a fellow of the IEEE, and a recipient of the ONR Young Investigator Awardin 2005 and the NSF CAREER award in 2003. He received the OutstandingResearch Award from the IEEE Phoenix Section in 2003. He is currently a Dis-tinguished Lecturer of the IEEE Communications Society.



Documents

Cascading effects in interdependent networks