Construction and properties of assortative random networks

TL;DR

This paper introduces an algorithm to modify the assortativity of networks, demonstrating how varying assortativity impacts network properties like diameter, clustering, and percolation behavior.

Contribution

The authors present a novel algorithm to control network assortativity and analyze its effects on network geometry and transport properties.

Findings

Assortativity significantly affects network diameter and clustering.

Degree of assortativity influences the size of the giant component.

Assortative networks show different percolation thresholds compared to uncorrelated networks.

Abstract

Many social networks exhibit assortative mixing so that the predictions of uncorrelated models might be inadequate. To analyze the role of assortativity we introduce an algorithm which changes correlations in a network and produces assortative mixing to a desired degree. This degree is governed by one parameter p. Changing this parameter one can construct networks ranging from fully random (p = 0) to totally assortative (p = 1). We apply the algorithm to a Barabasi-Albert scale-free network and show that the degree of assortativity is an important parameter governing geometrical and transport properties of networks. Thus, the diameter of the network and the clustering coefficient increase dramatically with the degree of assortativity. Moreover, the concentration dependences of the size of the giant component in the node percolation problem for uncorrelated and assortative networks are strongly different.