Undirected Congruence Model: Topological characteristics and epidemic spreading

In this paper, we investigate the topological characteristics of an undirected congruence network and the ability of the network against epidemic spreading. First, we construct a model of undirected congruence network and analyze its topological characteristics and deduce the upper bounds for the diameter and average path length respectively. We find that the undirected congruence network exhibits a likely power-law degree distribution. Then, we study the ability of the undirected congruence network against epidemic spreading by comparing it with other networks that are generated from the undirected congruence network by the degree-preserving rewiring algorithm. Our simulation results show that the undirected congruence network has a stronger ability to reduce the epidemic outbreaks than other networks. In particular, we find that the average size of the connected components of the attacked undirected congruence network is far larger than that of other attacked networks, which reveals that the cost of recovering the attacked undirected congruence network is far less than the other networks. Our study gains insight into the design of complex networks against epidemic spreading.