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k-core percolation and k-core organization of complex networks | | S.N. Dorogovtsev
; A.V. Goltsev
; J.F.F. Mendes
; | | Date: |
5 Sep 2005 | | Subject: | Statistical Mechanics; Mathematical Physics; Networking and Internet Architecture; Physics and Society | cond-mat.stat-mech cs.NI math-ph math.MP physics.soc-ph | | Abstract: | We present the solution of the k-core percolation problem for complex networks. We find variations of the k-core structure of randomly damaged uncorrelated networks, derive a criterion for the emergence of k-cores, and describe their structure. It turns out that random removal of vertices primarily destroys the k-core of the highest degree. We show that if the degree distribution of a network decreases sufficiently rapidly, the k-core percolation is a hybrid phase transition. If the second moment of the degree distribution diverges, the network contains an infinite sequence of k-cores which are ultra-robust against random damage. | | Source: | arXiv, cond-mat/0509102 | | Services: | Forum | Review | PDF | Favorites | |
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