Hopping in the crowd to unveil network topology

TL;DR

This paper models nonlinear diffusion on complex networks considering crowding effects, revealing how agent distribution relates to node connectivity, and introduces an inverse method to reconstruct network topology from limited measurements.

Contribution

It presents a novel nonlinear operator for diffusion under crowded conditions and develops an inverse approach to accurately reconstruct network connectivity from minimal data.

Findings

Asymptotic density saturates for high connectivity

Inverse method accurately reconstructs network degree distribution

Method successfully tested on synthetic and real data

Abstract

We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a constant value for sufficiently large connectivities, at variance with standard diffusion in the absence of excluded-volume effects. Building on this observation, we define and solve an inverse problem, aimed at reconstructing the a priori unknown connectivity distribution. The method gathers all the necessary information by repeating a limited number of independent measurements of the asymptotic density at a single node that can be chosen randomly. The technique is successfully tested against both synthetic and real data, and shown to estimate with great accuracy also the total number of nodes.