Ref Random Graphs

Newman, M. E. J., S. H. Strogatz and D. J. Watts (2001). Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E64: 026118 (17 pp.) (These authors studied graphs having distributions of vertex degree that were significantly different from those having the usual Poisson degree distributions. They develop the theory of random graphs with arbitrary degree distributions and examine simple undirected, unipartite graphs and directed and bipartite graphs deriving exact expressions for the location of the phase transition where a giant component first forms, the mean component size, the size of the giant component, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within the graph.)

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