A theoretical estimation for the optimal network robustness measure R against malicious node attacks

Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University Xian 710071, China

^(a) neouma@mail.xidian.edu.cn
neouma@163.com (corresponding author)

Received: 1 April 2015
Accepted: 21 July 2015

Abstract

In a recent work (Schneider C. M. et al., Proc. Natl. Acad. Sci. U.S.A., 108 (2011) 3838), Schneider et al. introduced an effective measure R to evaluate the network robustness against malicious attacks on nodes. Take R as the objective function, they used a heuristic algorithm to optimize the network robustness. In this paper, a theoretical analysis is conducted to estimate the value of R for different types of networks, including regular networks, WS networks, ER networks, and BA networks. The experimental results show that the theoretical value of R is approximately equal to that of optimized networks. Furthermore, the theoretical analysis also shows that regular networks are the most robust than other networks. To validate this result, a heuristic method is proposed to optimize the network structure, in which the degree distribution can be changed and the number of nodes and edges remains invariant. The optimization results show that the degree of most nodes in the optimal networks is close to the average degree, and the optimal network topology is close to regular networks, which confirms the theoretical analysis.