Properties of Random Graphs with Hidden Color

Details Properties of Random Graphs with Hidden Color Properties of Random Graphs with Hidden Color

2003-05-08

arxiv.org/abs/cond-mat/0305192v1

Physical Review E 68, 026107 (2003)

Physics

Condensed Matter

Statistical Mechanics

14 pages, LaTeX, no figures

Scientific paper

10.1103/PhysRevE.68.026107

We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global structural properties of graphs from the resulting ensembles is demonstrated. Cluster size statistics are derived with generating function techniques, yielding a well-defined percolation threshold. Explicit rules are derived for the enumeration of small subgraphs. Duality and redundancy is discussed, and subclasses corresponding to commonly studied models are identified.

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