Localized attack on clustering networks

Gaogao Dong, Huifang Hao, Ruijin Du, Shuai Shao, H. Eugene. Stanley, Havlin Shlomo

Clustering network is one of which complex network attracting plenty of scholars to discuss and study the structures and cascading process. We primarily analyzed the effect of clustering coefficient to other various of the single clustering network under localized attack. These network models including double clustering network and star-like NON with clustering and random regular (RR) NON of ER networks with clustering are made up of at least two networks among which exist interdependent relation among whose degree of dependence is measured by coupling strength. We show both analytically and numerically, how the coupling strength and clustering coefficient effect the percolation threshold, size of giant component, critical coupling point where the behavior of phase transition changes from second order to first order with the increase of coupling strength between the networks. Last, we study the two types of clustering network: one type is same with double clustering network in which each subnetwork satisfies identical degree distribution and the other is that their subnetwork satisfies different degree distribution. The former type is treated both analytically and numerically while the latter is treated only numerically. In each section, we compared two results obtained from localized attack and random attack according to Shao et al:[22].

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