Scale-free trees: the skeletons of complex networks

TL;DR

This paper studies the spanning trees of complex networks, revealing that scale-free trees and shortcuts form the network's backbone, with properties consistent across real-world and model networks, highlighting the role of betweenness centrality.

Contribution

It introduces a method to extract the communication kernel of networks via maximum betweenness centrality spanning trees, revealing universal scale-free properties and the significance of shortcuts.

Findings

Spanning trees exhibit scale-free betweenness centrality distribution.

Shortcut distribution influences network clustering and classification.

The method applies to both real-world and model networks.

Abstract

We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights are given by the edge betweenness centralities. We find that a scale-free tree and shortcuts organize a complex network. The spanning tree shows robust betweenness centrality distribution that was observed in scale-free tree models. It turns out that the shortcut distribution characterizes the properties of original network, such as the clustering coefficient and the classification of networks by the betweenness centrality distribution.