Tuning clustering in random networks with arbitrary degree distributions

TL;DR

This paper introduces a flexible generator for random networks with customizable degree distributions and clustering, revealing a universal relation between clustering and degree correlations that constrains network structure.

Contribution

It proposes a novel algorithm to generate networks with tunable clustering and degree distribution, uncovering a universal relation between clustering and degree correlations.

Findings

Universal relation between clustering and degree correlations.

Assortativity limits the level of clustering achievable.

Real networks observe the structural bounds predicted.

Abstract

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the clustering coefficient for each class of nodes of degree $k$ are fixed ad hoc and a priori. The algorithm generates corresponding topologies by applying first a closure of triangles and secondly the classical closure of remaining free stubs. The procedure unveils an universal relation among clustering and degree-degree correlations for all networks, where the level of assortativity establishes an upper limit to the level of clustering. Maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior. Correlation measures in real networks are seen to observe this structural bound.