Analytical results for stochastically growing networks: Connection to the zero-range process

Abstract

We introduce a stochastic model of growing networks where both the number of new nodes which join the network and the number of connections vary stochastically. We provide an exact mapping between this model and the zero-range process, and calculate analytically the degree distribution for any given evolution rule. We argue that this mapping can be used to infer a possible evolution rule for any given network. This is being demonstrated for a protein-protein interaction network of Saccharomyces cerevisiae.