A Tractable Complex Network Model based on the Stochastic Mean-field Model of Distance

TL;DR

This paper introduces a new stochastic mean-field model of distance for complex networks, providing a mathematically natural framework that captures key features like power-law degree distribution, clustering, and small diameter, with explicit calculations.

Contribution

It presents a simple two-parameter proportional attachment model within the stochastic mean-field framework, offering explicit analysis and broad feature compatibility.

Findings

Model captures power-law degree distribution

Model reproduces local clustering of edges

Model exhibits small network diameter

Abstract

Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We point out a new (in this context) platform for such models -- the stochastic mean-field model of distance -- and within this platform study a simple two-parameter proportional attachment model. The model is mathematicallly natural, permits a wide variety of explicit calculations, has the desired three qualitative features, and fits the complete range of degree scaling exponents and clustering parameters; in these respects it compares favorably to existing models.