Nongrowing Preferential Attachment Random Graphs

Abstract

We consider an edge rewiring process that is widely used to model the dynamics of scale-free weblike networks. This process uses preferential attachment and operates on sparse multigraphs with n vertices and m edges. We prove that its mixing time is optimal and develop a framework that simplifies the calculation of graph properties in the steady state. The applicability of this framework is demonstrated by calculating the degree distribution, the number of self-loops, and the threshold for the appearance of the giant component.