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Impact of Degree Heterogeneity on Attack Vulnerability of Interdependent Networks

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ABSTRACT

The study of interdependent networks has become a new research focus in recent years. We focus on one fundamental property of interdependent networks: vulnerability. Previous studies mainly focused on the impact of topological properties upon interdependent networks under random attacks, the effect of degree heterogeneity on structural vulnerability of interdependent networks under intentional attacks, however, is still unexplored. In order to deeply understand the role of degree distribution and in particular degree heterogeneity, we construct an interdependent system model which consists of two networks whose extent of degree heterogeneity can be controlled simultaneously by a tuning parameter. Meanwhile, a new quantity, which can better measure the performance of interdependent networks after attack, is proposed. Numerical simulation results demonstrate that degree heterogeneity can significantly increase the vulnerability of both single and interdependent networks. Moreover, it is found that interdependent links between two networks make the entire system much more fragile to attacks. Enhancing coupling strength between networks can greatly increase the fragility of both networks against targeted attacks, which is most evident under the case of max-max assortative coupling. Current results can help to deepen the understanding of structural complexity of complex real-world systems.

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Vulnerability of interdependent eba networks with different p after a fraction f of nodes removed from the networks with coupling strength q = 1.0.Different coupling types are considered separately: (a) random coupling; (b) assortative coupling; (c) disassortative coupling. All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations. The legends in (b,c) are the same as those of (a).
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f2: Vulnerability of interdependent eba networks with different p after a fraction f of nodes removed from the networks with coupling strength q = 1.0.Different coupling types are considered separately: (a) random coupling; (b) assortative coupling; (c) disassortative coupling. All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations. The legends in (b,c) are the same as those of (a).

Mentions: Figure 2 show the responses of fully interdependent eBA networks under targeted attacks on high-degree nodes with random (Fig. 2(a)), assortative (Fig. 2(b)) and disassortative (Fig. 2(c)) coupling, respectively. Considering the impact of degree heterogeneity of interdependent networks, as shown in Fig. 2, with all the three kinds of coupling, efficiency loss el of networks increases more rapidly with higher value of p, which demonstrates that corresponding networks are more vulnerable to attacks in targeted ways. Note that, this behavior is consistent with that of isolated eBA networks (Fig. 1).


Impact of Degree Heterogeneity on Attack Vulnerability of Interdependent Networks
Vulnerability of interdependent eba networks with different p after a fraction f of nodes removed from the networks with coupling strength q = 1.0.Different coupling types are considered separately: (a) random coupling; (b) assortative coupling; (c) disassortative coupling. All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations. The legends in (b,c) are the same as those of (a).
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC5016735&req=5

f2: Vulnerability of interdependent eba networks with different p after a fraction f of nodes removed from the networks with coupling strength q = 1.0.Different coupling types are considered separately: (a) random coupling; (b) assortative coupling; (c) disassortative coupling. All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations. The legends in (b,c) are the same as those of (a).
Mentions: Figure 2 show the responses of fully interdependent eBA networks under targeted attacks on high-degree nodes with random (Fig. 2(a)), assortative (Fig. 2(b)) and disassortative (Fig. 2(c)) coupling, respectively. Considering the impact of degree heterogeneity of interdependent networks, as shown in Fig. 2, with all the three kinds of coupling, efficiency loss el of networks increases more rapidly with higher value of p, which demonstrates that corresponding networks are more vulnerable to attacks in targeted ways. Note that, this behavior is consistent with that of isolated eBA networks (Fig. 1).

View Article: PubMed Central - PubMed

ABSTRACT

The study of interdependent networks has become a new research focus in recent years. We focus on one fundamental property of interdependent networks: vulnerability. Previous studies mainly focused on the impact of topological properties upon interdependent networks under random attacks, the effect of degree heterogeneity on structural vulnerability of interdependent networks under intentional attacks, however, is still unexplored. In order to deeply understand the role of degree distribution and in particular degree heterogeneity, we construct an interdependent system model which consists of two networks whose extent of degree heterogeneity can be controlled simultaneously by a tuning parameter. Meanwhile, a new quantity, which can better measure the performance of interdependent networks after attack, is proposed. Numerical simulation results demonstrate that degree heterogeneity can significantly increase the vulnerability of both single and interdependent networks. Moreover, it is found that interdependent links between two networks make the entire system much more fragile to attacks. Enhancing coupling strength between networks can greatly increase the fragility of both networks against targeted attacks, which is most evident under the case of max-max assortative coupling. Current results can help to deepen the understanding of structural complexity of complex real-world systems.

No MeSH data available.