Distance distribution in configuration model networks

TL;DR

This paper derives analytical expressions for the distribution of shortest path lengths in configuration model networks, linking it to degree distribution moments, and validates results with simulations.

Contribution

It introduces recursive equations to analytically determine shortest path length distributions in various configuration model networks, including degenerate, binomial, and power-law types.

Findings

Analytical expressions match numerical simulations.

Distribution measures are linked to degree distribution moments.

Results apply to networks with diverse degree distributions.

Abstract

We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical simulations for networks with degenerate, binomial and power-law degree distributions. The mean, mode and variance of the distribution of shortest path lengths are also evaluated. These results provide expressions for central measures and dispersion measures of the distribution of shortest path lengths in terms of moments of the degree distribution, illuminating the connection between the two distributions.