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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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The critical values fc as a function of the coupling strength q and model parameter p.Different coupling types are considered separately: (a) random coupling; (b) max-max coupling; (c) min-min coupling; (d) max-min coupling; (e) min-max coupling. All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations.
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f3: The critical values fc as a function of the coupling strength q and model parameter p.Different coupling types are considered separately: (a) random coupling; (b) max-max coupling; (c) min-min coupling; (d) max-min coupling; (e) min-max coupling. All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations.

Mentions: In order to explore the influence of both degree heterogeneity and interdependency, numerical simulations are performed to examine the responses of partially interdependent networks. Figure 3 presents the values of fc as functions of coupling strength q and parameter p of interdependent networks with different coupling types: random coupling (Fig. 3(a)), max-max coupling (Fig. 3(b)), min-min coupling (Fig. 3(c)), max-min coupling (Fig. 3(d)), min-max coupling (Fig. 3(e)). All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations.


Impact of Degree Heterogeneity on Attack Vulnerability of Interdependent Networks
The critical values fc as a function of the coupling strength q and model parameter p.Different coupling types are considered separately: (a) random coupling; (b) max-max coupling; (c) min-min coupling; (d) max-min coupling; (e) min-max coupling. All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: The critical values fc as a function of the coupling strength q and model parameter p.Different coupling types are considered separately: (a) random coupling; (b) max-max coupling; (c) min-min coupling; (d) max-min coupling; (e) min-max coupling. All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations.
Mentions: In order to explore the influence of both degree heterogeneity and interdependency, numerical simulations are performed to examine the responses of partially interdependent networks. Figure 3 presents the values of fc as functions of coupling strength q and parameter p of interdependent networks with different coupling types: random coupling (Fig. 3(a)), max-max coupling (Fig. 3(b)), min-min coupling (Fig. 3(c)), max-min coupling (Fig. 3(d)), min-max coupling (Fig. 3(e)). All the networks are with N = 2000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations.

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.