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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.

No MeSH data available.


Vulnerability of single eba networks with different p after a fraction f of nodes removed from the networks.(a) The relative size S of the giant connected component; (b) Efficiency loss (el); (c) Number of isolated connected components (Ns); (d) Average size of isolated connected components (〈s〉). All the networks are with N = 10000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations.
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f1: Vulnerability of single eba networks with different p after a fraction f of nodes removed from the networks.(a) The relative size S of the giant connected component; (b) Efficiency loss (el); (c) Number of isolated connected components (Ns); (d) Average size of isolated connected components (〈s〉). All the networks are with N = 10000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations.

Mentions: Firstly, numerical simulations are performed to investigate the effect of degree heterogeneity on single complex networks. The responses of single eBA networks under targeted node removal are exhibited in Fig. 1. All the initial networks (N = 10,000 and 〈k〉 = 6) are constructed by eBA model with m = 3. Each point is averaged over 10 independent realizations.


Impact of Degree Heterogeneity on Attack Vulnerability of Interdependent Networks
Vulnerability of single eba networks with different p after a fraction f of nodes removed from the networks.(a) The relative size S of the giant connected component; (b) Efficiency loss (el); (c) Number of isolated connected components (Ns); (d) Average size of isolated connected components (〈s〉). All the networks are with N = 10000 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

f1: Vulnerability of single eba networks with different p after a fraction f of nodes removed from the networks.(a) The relative size S of the giant connected component; (b) Efficiency loss (el); (c) Number of isolated connected components (Ns); (d) Average size of isolated connected components (〈s〉). All the networks are with N = 10000 and 〈k〉 = 6. Each point is averaged over 10 independent realizations.
Mentions: Firstly, numerical simulations are performed to investigate the effect of degree heterogeneity on single complex networks. The responses of single eBA networks under targeted node removal are exhibited in Fig. 1. All the initial networks (N = 10,000 and 〈k〉 = 6) are constructed by eBA model with m = 3. 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.