Authors: Yilun Shang
Addresses: Institute for Cyber Security, University of Texas at San Antonio, San Antonio, Texas 78249, USA
Abstract: 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.
Keywords: natural connectivity; Estrada index; scale-free networks; percolation; bipartite networks; degree-dependent failure; network failure; network fragility; network robustness; numerical simulation.
International Journal of Simulation and Process Modelling, 2013 Vol.8 No.1, pp.74 - 78
Available online: 22 Jul 2013 *Full-text access for editors Access for subscribers Purchase this article Comment on this article