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      Spectra of random graphs with arbitrary expected degrees

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      Physical Review E
      American Physical Society (APS)

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          A critical point for random graphs with a given degree sequence

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            Synchronization in complex networks

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              Random graphs with arbitrary degree distributions and their applications.

              Recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the world-wide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
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                Author and article information

                Journal
                PLEEE8
                Physical Review E
                Phys. Rev. E
                American Physical Society (APS)
                1539-3755
                1550-2376
                January 2013
                January 10 2013
                : 87
                : 1
                Article
                10.1103/PhysRevE.87.012803
                7e69b51d-071b-4527-9434-c0238c863bd2
                © 2013

                http://link.aps.org/licenses/aps-default-license

                http://link.aps.org/licenses/aps-default-accepted-manuscript-license

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