Scaling of degree correlations and the influence on diffusion in scale-free networks

TL;DR

This paper uses scaling theory to analyze degree correlations in scale-free networks, revealing how these correlations influence network structure and diffusion processes, with implications for robustness and information spread.

Contribution

It provides a theoretical framework to classify scale-free networks based on their degree correlations, linking structural properties to diffusion dynamics.

Findings

Social networks and Internet are close to random networks with connected hubs.

Biological networks and WWW show strong anti-correlations.

Anti-correlations accelerate diffusion processes.

Abstract

Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here, we use scaling theory to quantify the degree of correlations in the particular case of networks with a power-law degree distribution. These networks are classified in terms of their correlation properties, revealing additional information on their structure. For instance, the studied social networks and the Internet at the router level are clustered around the line of random networks, implying a strongly connected core of hubs. On the contrary, some biological networks and the WWW exhibit strong anti-correlations. The present approach can be used to study robustness or diffusion, where we find that anti-correlations tend to accelerate the diffusion process.