Scale-free trees: The skeletons of complex networks

The properties of the spanning trees of various real-world and model networks were investigated. The determination of the spanning tree representing the communication kernel of the original network, by maximizing the total weight of the edges, whose weight were given by the edge betweenness centralities, was also presented. It was found that a scale-free tree and shortcuts organize a complex network. It was observed that the scale-free spanning tree shows very robust betweenness centrality distributions and the remaining shortcuts characterize the properties of the original network, in ubiquitous scale-free networks.