Correlation distances in social networks

TL;DR

This paper investigates degree assortativity in social and complex networks, extending traditional definitions, and finds that positive degree correlations diminish beyond immediate neighbors, with some evidence of disassortativity at larger distances.

Contribution

It introduces an extended measure of degree assortativity beyond nearest neighbors and compares model and real networks, revealing how correlations change with distance.

Findings

Degree correlations decrease after one step in social networks.

Real networks show no correlations beyond nearest neighbors.

Nodes three steps apart tend to be disassortative.

Abstract

In this work we explore degree assortativity in complex networks, and extend its usual definition beyond that of nearest neighbours. We apply this definition to model networks, and describe a rewiring algorithm that induces assortativity. We compare these results to real networks. Social networks in particular tend to be assortatively mixed by degree in contrast to many other types of complex networks. However, we show here that these positive correlations diminish after one step and in most of the empirical networks analysed. Properties besides degree support this, such as the number of papers in scientific coauthorship networks, with no correlations beyond nearest neighbours. Beyond next-nearest neighbours we also observe a diasassortative tendency for nodes three steps away indicating that nodes at that distance are more likely different than similar.