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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 dependencies of  and kmax on parameter p of eBA networks with N = 10,000 and .
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f5: The dependencies of and kmax on parameter p of eBA networks with N = 10,000 and .

Mentions: In order to further study the effects of p on degree heterogeneity, two important indicators, and kmax of the resultant networks are examined. kmax means the maximal value of the node degree in the whole network. is defined to be the variance of node degree sequence, i.e., . Figure 5 shows the dependencies of and kmax on p. For 0 ≤ p ≤ 1, as p increases, is observed to increase monotonously, implying the increase of degree heterogeneity (see Fig. 5(a)). Meanwhile, with increasing p, kmax also becomes larger (see Fig. 5(b)). The increase of kmax with increasing p indicates the emergence of hub nodes, which have much more connections than the others. These results verify that a higher value of p makes corresponding eBA network more heterogeneous in connectivity.


Impact of Degree Heterogeneity on Attack Vulnerability of Interdependent Networks
The dependencies of  and kmax on parameter p of eBA networks with N = 10,000 and .
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: The dependencies of and kmax on parameter p of eBA networks with N = 10,000 and .
Mentions: In order to further study the effects of p on degree heterogeneity, two important indicators, and kmax of the resultant networks are examined. kmax means the maximal value of the node degree in the whole network. is defined to be the variance of node degree sequence, i.e., . Figure 5 shows the dependencies of and kmax on p. For 0 ≤ p ≤ 1, as p increases, is observed to increase monotonously, implying the increase of degree heterogeneity (see Fig. 5(a)). Meanwhile, with increasing p, kmax also becomes larger (see Fig. 5(b)). The increase of kmax with increasing p indicates the emergence of hub nodes, which have much more connections than the others. These results verify that a higher value of p makes corresponding eBA network more heterogeneous in connectivity.

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.