Pair Correlations in Scale-Free Networks

TL;DR

This paper investigates degree correlations in scale-free networks, revealing disassortative and neutral regions, and extends the analysis to other properties and bipartite networks, combining analytical and simulation methods.

Contribution

It provides a comprehensive analysis of degree correlations in the BA model and introduces a new correlation measurement for bipartite networks.

Findings

Disassortative correlation for low degrees

Neutral correlation for high degrees

Average neighbor degree diverges in large networks

Abstract

Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi-Albert (BA) Scale-Free model with both analytical results and simulations, and find two neighboring regions, a disassortative one for low degrees and a neutral one for high degrees. The average degree of the neighbors of a randomly picked node is expected to diverge in the limit of infinite network size. As an generalization of the concept of correlation, we also study the correlations of other scalar properties, including age and clustering coefficient. Finally we propose a correlation measurement in bipartite networks.