Heterogeneous network with distance dependent connectivity

TL;DR

This paper studies a spatial network model where connection probability depends on distance, showing how to introduce heterogeneity to produce fat-tailed degree distributions while preserving small-world properties.

Contribution

The paper introduces a generalized spatial network model with distance-dependent connectivity that achieves fat-tailed degree distributions without losing small-world characteristics.

Findings

Degree distribution is sharply peaked in the basic model.

Heterogeneity leads to fat-tailed degree distributions.

Small-world properties are maintained with heterogeneity.

Abstract

We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the basic model is sharply peaked around its mean value. Since the model was originally developed to mimic the social network of acquaintances, to broaden the degree distribution we propose its generalization. We show that when heterogeneity is introduced to the model, it is possible to obtain fat tails of the degree distribution. Meanwhile, the small-world phenomenon present in the basic model is not affected. To support our claims, both analytical and numerical results are obtained.