Maximum Entropy Models of Shortest Path and Outbreak Distributions in Networks

TL;DR

This paper introduces a maximum entropy-based model for shortest path length distributions in networks, linking network topology to spreading dynamics, and establishes the generalized Gamma distribution as a key descriptor, supported by experimental validation.

Contribution

It develops a novel maximum entropy framework to model shortest path distributions and identifies the generalized Gamma distribution as a universal descriptor for arbitrary networks.

Findings

Generalized Gamma distribution accurately models shortest path histograms.

Maximum entropy approach provides a physically plausible network characterization.

Experimental results support theoretical predictions.

Abstract

Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average as well as maximum distances can be determined therefrom; on the other hand, they are closely related to the dynamics of network spreading processes. Because of the combinatorial nature of networks, we apply maximum entropy arguments to derive a general, physically plausible model. In particular, we establish the generalized Gamma distribution as a continuous characterization of shortest path length histograms of networks or arbitrary topology. Experimental evaluations corroborate our theoretical results.