Classification of scale-free networks

TL;DR

This paper introduces a new classification method for scale-free networks based on the power-law distribution of betweenness centrality, revealing two universal classes with distinct topological and resilience features.

Contribution

It demonstrates that betweenness centrality distribution can classify scale-free networks into two universal classes, providing insights into their topology and robustness.

Findings

Two universality classes with ta  2.2 and 2.0 identified.

Real-world networks categorized into these classes based on betweenness centrality.

Distinct topological and resilience features observed between the classes.

Abstract

While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is robust and use it to classify the scale-free networks. We have observed two universality classes with \eta \approx 2.2(1) and 2.0, respectively. Real world networks for the former are the protein interaction networks, the metabolic networks for eukaryotes and bacteria, and the co-authorship network, and those for the latter one are the Internet, the world-wide web, and the metabolic networks for archaea. Distinct features of the mass-distance relation, generic topology of geodesics and resilience under attack of the two classes are identified. Various model networks also belong to either of the two classes while their degree exponents are tunable.