A repair strategy to the attacked random and scale-free networks

L. P. Chi; C. B. Yang; X. Cai

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arXiv · cond-mat/0611389

A repair strategy to the attacked random and scale-free networks

L. P. Chi·C. B. Yang·X. Cai

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Abstract

With a simple attack and repair evolution model, we investigate the stability and structural changes of the Erdos-Renyi random graphs (RG) and Barabasi-Albert scale-free (SF) networks. We introduce a new quantity, invulnerability I(s), to describe the stability of the system. We find that both RG and SF networks can evolve to a stationary state. The stationary value I_c has a power-law dependence on the repair probability p_re. We also analyze the effects of the repair strategy to the attack tolerance of the networks. We observe that there is a threshold, (k_max)_c, for the maximum degree. The maximum degree k_max at time s will be no smaller than (k_max)_c. We give further information on the evolution of the networks by comparing the changes of the topological parameters, such as degree distribution P(k), average degree , shortest path length L, clustering coefficient C, assortativity r, under the initial and stationary states.

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L. P. Chi, C. B. Yang, X. Cai. 2006-11-15. A repair strategy to the attacked random and scale-free networks. https://arxiv.org/abs/cond-mat/0611389

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