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Random Graphs with Clustering

M. E. J. Newman
Phys. Rev. Lett. 103, 058701 – Published 27 July 2009
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Abstract

We offer a solution to a long-standing problem in the theory of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity—the propensity for two neighbors of a network node also to be neighbors of one another. We show how standard random-graph models can be generalized to incorporate clustering and give exact solutions for various properties of the resulting networks, including sizes of network components, size of the giant component if there is one, position of the phase transition at which the giant component forms, and position of the phase transition for percolation on the network.

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  • Received 29 March 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.058701

©2009 American Physical Society

Synopsis

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Neighborly networks

Published 3 August 2009

A different way of modeling networks allows an exact derivation of their properties.

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Authors & Affiliations

M. E. J. Newman

  • Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA, and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

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Issue

Vol. 103, Iss. 5 — 31 July 2009

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