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Metric structure of random networks

S. N. Dorogovtsev·J. F. F. Mendes·A. N. Samukhin
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Abstract

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.

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BibTeXRIS

S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin. 2002-11-28. Metric structure of random networks. https://doi.org/10.1016/s0550-3213(02)01119-7

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