Percolation on bipartite scale-free networks

TL;DR

This paper analyzes how biased edge removal affects the connectivity of bipartite scale-free networks, revealing critical phenomena and phase transitions using generating functions and Potts model techniques.

Contribution

It introduces an analytical framework for biased percolation on bipartite scale-free networks, deriving exact equations and critical exponents for the percolation transition.

Findings

Percolation transition depends on the bias parameter alpha.

Exact self-consistent equations describe the macroscopic behavior.

Critical exponents are derived using Potts model connections.

Abstract

Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type. Such bipartite graphs appear in many social networks, for instance in affiliation networks and in sexual contact networks in which both types of nodes show the scale-free characteristic for the degree distribution. During the depreciation process, an edge between nodes with degrees k and q is retained with probability proportional to (kq)^(-alpha), where alpha is positive so that links between hubs are more prone to failure. The removal process is studied analytically by introducing a generating functions theory. We deduce exact self-consistent equations describing the system at a macroscopic level and discuss the percolation transition. Critical exponents are obtained by exploiting the Fortuin-Kasteleyn construction which provides a link between our model and a limit of the Potts model.