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 International Conference on Complex Systems (ICCS2007)

structure of complex networks

José Mendes
University of Aveiro

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     Last modified: August 27, 2007

The k-core decomposition was recently applied to a number of real-world networks. Rich k-core architectures of real networks were revealed. We find the structure of k-cores, their sizes, and their birth points — the bootstrap percolation thresholds. I will show a derivation of exact equations describing the k-core organization of a randomly damaged uncorrelated network with an arbitrary degree distribution. This allows us to obtain the sizes and other structural characteristics of k-cores in a variety of damaged and undamaged random networks and find the nature of the k-core percolation in complex networks. These general results will be applied to the classical random graphs and to scale-free networks, in particular, to empirical router-level Internet maps.

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