Measuring degree-dependent failure in scale-free networks of bipartite structure. (2013)

• Record Type: Journal Article
• Authors: Shang*, Yilun
• Is Part Of: International journal of simulation and process modelling. Volume 8:Number 1(2013)
• Publication Date: 2013
• Subjects: bipartite networks. -- Estrada index -- natural connectivity -- percolation -- scale-free networks; Management -- Computer simulation -- Periodicals; Mathematical models -- Periodicals; Operations research -- Periodicals; Simulation methods -- Periodicals; 003.05
• Languages: English
• ISSNs: 1740-2123

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.