Uncovering disassortativity in large scale-free networks

TL;DR

This paper introduces a new method using rank correlation measures like Spearman's rho to accurately assess degree-degree dependencies in large networks, overcoming size-related limitations of traditional assortativity coefficients.

Contribution

It proposes and validates a size-independent measure for network mixing patterns, revealing stronger disassortativity in web graphs than previously detected.

Findings

Spearman's rho provides consistent dependency measures across different network sizes.

Disassortativity in web graphs is stronger than earlier believed.

Traditional assortativity coefficients decrease with network size, leading to misleading conclusions.

Abstract

Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree dependencies between neighbouring nodes. In this paper we propose a new way of measuring degree-degree dependencies. One of the problems with the commonly used assortativity coefficient is that in disassortative networks its magnitude decreases with the network size. We mathematically explain this phenomenon and validate the results on synthetic graphs and real-world network data. As an alternative, we suggest to use rank correlation measures such as Spearman's rho. Our experiments convincingly show that Spearman's rho produces consistent values in graphs of different sizes but similar structure, and it is able to reveal strong (positive or negative) dependencies in large graphs. In particular, we discover much stronger negative degree-degree dependencies} in Web graphs than was previously thought. {Rank correlations allow us to compare the assortativity of networks of different sizes, which is impossible with the assortativity coefficient due to its genuine dependence on the network size. We conclude that rank correlations provide a suitable and informative method for uncovering network mixing patterns.