  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.
