Scale-free trees: the skeletons of complex 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.