Small worlds and clustering in spatial networks

TL;DR

This paper investigates spatial network models that naturally exhibit key real-world properties like sparsity, small-world characteristics, and clustering by using a maximum entropy framework with energy-dependent link formation.

Contribution

It identifies a broad class of spatial network models that are sparse, small-world, and have nonzero clustering in the thermodynamic limit, advancing understanding of spatial network properties.

Findings

Models can reproduce real-world network properties

Maximum entropy approach links energy dependence to network features

Spatial heterogeneity affects clustering and small-worldness

Abstract

Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current surge of activity in graph embedding. In the vast realm of spatial network models, only a few reproduce even the most basic properties of real-world networks. Here, we focus on three such properties---sparsity, small worldness, and clustering---and identify the general subclass of spatial homogeneous and heterogeneous network models that are sparse small worlds and that have nonzero clustering in the thermodynamic limit. We rely on the maximum entropy approach where network links correspond to noninteracting fermions whose energy dependence on spatial distances determines network small worldness and clustering.