Topology and correlations in structured scale-free networks

TL;DR

This paper analyzes a class of structured scale-free networks with high clustering and correlations, providing exact solutions for low connectivity cases and revealing the absence of small-world properties across parameters.

Contribution

It offers an exact analytical study of a new class of scale-free networks, detailing their clustering, correlations, and lack of small-world features.

Findings

Connectivity distribution depends on model details

Exact solutions for low average connectivity

Networks lack small-world properties

Abstract

We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the model. We solve exactly the case of low average connectivity, providing also exact expressions for the clustering and degree correlation functions. The model also exhibits a lack of small world properties in the whole parameters range. We discuss the physical properties of these networks in the light of the present detailed analysis.