Pursuit-Evasion in models of complex networks

Abstract

Pursuit-evasion games, such as the game of Cops and Robbers, are a simplified model for network security. In this game, cops try to capture a robber loose on the vertices of the network. The minimum number of cops required to win on a graph G is its number. We present asymptotic results for the game of Cops and Robbers played in various stochastic network models, such as in G(n, p) with nonconstant p and in random power-law graphs. We find bounds for the cop number of G(n, p) for a large range p as a function of n. We prove that the cop number of random power-law graphs with n vertices is asymptotically almost surely Θ(n). The cop number of the core of random power-law graphs is investigated, and it is proved to be of smaller order than the order of the core. © A K Peters, Ltd.