Circuits in random graphs: from local trees to global loops

Details Circuits in random graphs: from local trees to global loops Circuits in random graphs: from local trees to global loops

2004-07-09

arxiv.org/abs/cond-mat/0407253v1

Journal of Statistical Mechanics: Theory and Experiment (2004) P09004

Physics

Condensed Matter

Statistical Mechanics

submitted to JSTAT

Scientific paper

10.1088/1742-5468/2004/09/P09004

We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one side we obtain analytic results for the infinite volume limit in agreement with existing exact results. On the other side we implement a counting algorithm, enumerate circuits at finite N and draw some general conclusions about the finite N behavior of the circuits.

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