Scale-free spanning trees of complex networks

We investigate the properties of spanning trees of complex networks. We construct spanning trees with a maximum total weight of edges that is given by average traffic, called "edge betweenness centrality". The resulting spanning tree is found to represent the communication kernel of networks and the degree distribution of spanning trees shows scale-free behavior for many model and real-world networks. The degree of the spanning trees has strong correlation with their original network topology. We also study other methods of constructing spanning trees, based on random choice of edge removal, called "self-repairing bond percolation", and the subsequent burning from a single vertex. We find that the scale-free behavior of the spanning trees does not depend on construction methods.