Random graphs with clustering

Details Random graphs with clustering Random graphs with clustering

2009-03-24

arxiv.org/abs/0903.4009v1

Phys. Rev. Lett. 103, 058701 (2009)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.103.058701

We offer a solution to a long-standing problem in the physics 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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