Robustness of networks against viruses: the role of the spectral radius

In this paper we study the spectral radius of a number of real-life networks. This study is motivated by the fact that the smaller the spectral radius, the higher the robustness of a network against the spread of viruses. First we study how well-known upper bounds for the spectral radius of graphs match to the spectral radii of the social network of the Dutch soccer team, the Dutch roadmap network, the network of the observable part of the Internet graph at the IP-level and the autonomous system level. Secondly, we compare the spectral radius for these real-life networks with those of commonly used complex network models