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The robustness of a network is depending on the type of attack we areconsidering. In this paper we focus on the spread of viruses on networks. It iscommon practice to use the epidemic threshold as a measure for robustness.Because the epidemic threshold is inversely proportional to the largesteigenvalue of the adjacency matrix, it seems easy to compare the robustness oftwo networks. We will show in this paper that the comparison of the robustnesswith respect to virus spread for two networks actually depends on the value ofthe effective spreading rate tau. For this reason we propose a new metric, theviral conductance, which takes into account the complete range of values taucan obtain. In this paper we determine the viral conductance of regular graphs,complete bi-partite graphs and a number of realistic networks.

A new metric for robustness with respect to virus spread