Journal
NUCLEAR PHYSICS B
Volume 653, Issue 3, Pages 307-338Publisher
ELSEVIER
DOI: 10.1016/S0550-3213(02)01119-7
Keywords
random geometry; random graphs; intervertex distance; connected components
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We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the distribution of shortest-path lengths (intervertex distances) in these networks and a number of related characteristics for the networks with various degree distributions. We show that in the large network limit this extremely narrow intervertex distance distribution has a finite width while the mean intervertex distance grows with the size of a network. The size dependence of the mean intervertex distance is discussed in various situations. (C) 2002 Elsevier Science B.V. All rights reserved.
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