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.
- Received 29 March 2009
DOI:https://doi.org/10.1103/PhysRevLett.103.058701
©2009 American Physical Society
Synopsis
Neighborly networks
Published 3 August 2009
A different way of modeling networks allows an exact derivation of their properties.
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