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

TL;DR

This paper introduces a stochastic model for growing networks, establishes an exact mapping to the zero range process, and derives analytical degree distributions, enabling inference of network evolution rules, demonstrated on yeast PPI networks.

Contribution

It provides a novel analytical framework linking network growth to zero range processes, allowing for precise degree distribution calculations and network evolution inference.

Findings

Derived exact degree distribution formulas for the model.

Mapped network growth dynamics to zero range process.

Applied method to real protein interaction network data.

Abstract

We introduce a stochastic model of growing networks where both, the number of new nodes which joins the network and the number of connections, vary stochastically. We provide an exact mapping between this model and zero range process, and use this mapping to derive an analytical solution of degree distribution for any given evolution rule. One can also use this mapping to infer about a possible evolution rule for a given network. We demonstrate this for protein-protein interaction (PPI) network for Saccharomyces Cerevisiae.