Global core, and galaxy structure of networks

We propose a novel approach, namely local reduction of networks, to extract the global core (GC, for short) from a complex network. The algorithm is built based on the small community phenomenon of networks. The global cores found by our local reduction from some classical graphs and benchmarks convince us that the global core of a network is intuitively the supporting graph of the network, which is "similar to" the original graph, that the global core is small and essential to the global properties of the network, and that the global core, together with the small communities gives rise to a clear picture of the structure of the network, that is, the galaxy structure of networks. We implement the local reduction to extract the global cores for a series of real networks, and execute a number of experiments to analyze the roles of the global cores for various real networks. For each of the real networks, our experiments show that the found global core is small, that the global core is similar to the original network in the sense that it follows the power law degree distribution with power exponent close to that of the original network, that the global core is sensitive to errors for both cascading failure and physical attack models, in the sense that a small number of random errors in the global core may cause a major failure of the whole network, and that the global core is a good approximate solution to the r-radius center problem, leading to a galaxy structure of the network.