A new metric for robustness with respect to virus spread

TL;DR

This paper introduces the viral conductance metric to evaluate network robustness against virus spread across all possible spreading rates, improving upon the epidemic threshold measure.

Contribution

It proposes a new robustness metric, viral conductance, that considers the entire range of spreading rates, unlike the traditional epidemic threshold.

Findings

Viral conductance varies significantly across different network types.

Regular graphs and bipartite graphs have distinct viral conductance profiles.

The metric provides a comprehensive robustness measure for realistic networks.

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 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.