A new metric for robustness with respect to virus spread

Abstract

The robustness of a network is depending on the type of attack we
are considering. In this paper we focus on the spread of viruses on networks. It
is common practice to use the epidemic threshold as a measure for robustness.
Because the epidemic threshold is inversely proportional to the largest eigenvalue
of the adjacency matrix, it seems easy to compare the robustness of two
networks. We will show in this paper that the comparison of the robustness with
respect to virus spread for two networks actually depends on the value of the effective
spreading rate ¿. For this reason we propose a new metric, the viral conductance,
which takes into account the complete range of values ¿ can obtain. In
this paper we determine the viral conductance of regular graphs, complete bipartite
graphs and a number of realistic networks.