Title: Measuring degree-dependent failure in scale-free networks of bipartite structure

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), 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.

DOI: 10.1504/IJSPM.2013.055191

International Journal of Simulation and Process Modelling, 2013 Vol.8 No.1, pp.74 - 78

Available online: 22 Jul 2013 *

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