  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 tau. For this reason we propose a new metric, the
viral conductance, which takes into account the complete range of values tau
can obtain. In this paper we determine the viral conductance of regular graphs,
complete bi-partite graphs and a number of realistic networks.
