Stability of complex networks under the evolution of attack and repair

TL;DR

This paper studies the stability of Erdos-Renyi and Barabasi-Albert networks under attack and repair, introducing a new stability measure and analyzing their evolution to stationary states with different topological features.

Contribution

It introduces the invulnerability I(s) metric and compares the stability and topological changes of RG and SF networks under attack-repair dynamics.

Findings

Both network types reach stationary states.

Stationary invulnerability depends on network parameters.

Networks become more clustered and assortative after evolution.

Abstract

With a simple attack and repair evolution model, we investigate and compare the stability 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 Ic has a power-law dependence on the average degree <k>_rg for RG networks; and an exponential relationship with the repair probability p_sf for SF networks. We also discuss the topological changes of RG and SF networks between the initial and stationary states. We observe that the networks in the stationary state have smaller average degree <k> but larger clustering coefficient C and stronger assortativity r.