Mixing patterns in networks

TL;DR

This paper investigates assortative mixing in various networks, introduces measures for different types of mixing, and explores how assortativity affects network properties and resilience through models and real-world data.

Contribution

It presents new measures for assortative mixing, applies them to real networks, and develops models to analyze how assortativity influences network structure and robustness.

Findings

Assortative mixing is common in many real-world networks.

Mixing by degree significantly affects network resilience.

Models show how varying assortativity alters network connectivity.

Abstract

We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age. As a special example of the latter we consider mixing according to vertex degree, i.e., according to the number of connections vertices have to other vertices: do gregarious people tend to associate with other gregarious people? We propose a number of measures of assortative mixing appropriate to the various mixing types, and apply them to a variety of real-world networks, showing that assortative mixing is a pervasive phenomenon found in many networks. We also propose several models of assortatively mixed networks, both analytic ones based on generating function methods, and numerical ones based on Monte Carlo graph generation techniques. We use these models to probe the properties of networks as their level of assortativity is varied. In the particular case of mixing by degree, we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices.