Measuring degree-dependent failure in scale-free networks of bipartite structure. (2013) - Shang*, Yilun
We study degree-dependent failure in networks consisting of two types of nodes with edges running only between nodes of unlike type. Both types of nodes are assumed to have scale-free degree distributions. These networks are called scale-free bipartite graphs, which appear in many real-life networks. In this article, we measure network robustness and fragility based on a recently proposed spectral measure, natural connectivity, which is an average eigenvalue obtained from the graph spectrum. During the edge removal process, an edge between nodes with degrees k and l is retained with a probability proportional to ( kl ) – α, where α > 0 is a biased exponent, so that the most connected nodes are depreciated first. A clear division between robust regime and fragile regime can be extracted based on natural connectivity by tuning the exponent α. The theory is verified by the numerical simulations.