2008/12/10 by Robert E. Kooij, Robert Kooij, Phillip Schumm +4
Computer Science · Engineering · Mathematics · Medicine · #Artificial Immune Systems Applications #COVID-19 epidemiological studies #D.2.8 #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Mathematical and Theoretical Epidemiology and Ecology Models #cs.DM
paper · pdf · doi:10.48550/arxiv.0812.1908
12 pages, 4 figures
arxiv created 2008/12/10 · openalex publication_date 2008/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.