The Yule distribution and frailty--a note on spurious preferential attachment

TL;DR

This paper proposes an alternative to preferential attachment for explaining power law networks, using a randomized Poisson process to model link growth rates, and demonstrates its similarities and differences through analytical and simulation methods.

Contribution

It introduces a novel stochastic model based on a Poisson process that reproduces the degree distribution of preferential attachment networks, providing new insights into network growth mechanisms.

Findings

The Poisson-based model reproduces the degree distribution of preferential attachment.

Simulations show similar degree distributions and growth rates in both models.

Structural differences are identified through joint degree distribution and network coreness analysis.

Abstract

Preferential attachment is a popular generative mechanism to explain the widespread observation of power law distributed networks. We introduce an alternative explanation for the phenomenon by allowing the link growth rates to vary across the nodes according to a randomized Poisson process. The distribution of rates, which reproduces the degree distribution of a preferential attachment process (Yule process) is derived analytically. We demonstrate with use of simulations that the degree distribution and growth rates in single time intervals are similar for the random process and the preferential attachment process. Structural differences are analyzed by examining the joint degree distribution and network coreness.