Random Graphs with Hidden Color

Details Random Graphs with Hidden Color Random Graphs with Hidden Color

2003-03-21

arxiv.org/abs/cond-mat/0303466v1

Physical Review E 68, 015102 (2003)

Physics

Condensed Matter

Statistical Mechanics

4 pages, no figures, RevTeX

Scientific paper

10.1103/PhysRevE.68.015102

We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a nontrivial correlation structure in the resulting graphs. The approach unifies a number of existing random graph ensembles within a common general formalism, and allows for the analytic calculation of observable graph characteristics. In particular, generating function techniques are used to derive the size distribution of connected components (clusters) as well as the location of the percolation threshold where a giant component appears.

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