An algorithm for counting circuits: application to real-world and random graphs

Details An algorithm for counting circuits: application to real-world and random graphs An algorithm for counting circuits: application to real-world and random graphs

2005-07-22

arxiv.org/abs/cond-mat/0507525v2

Europhys. Lett. 73, 8 (2006)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 3 figures, minor corrections, accepted version

Scientific paper

10.1209/epl/i2005-10355-0

We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world networks, it allows to estimate exponentially large numbers of circuits in polynomial time. We illustrate the method by studying a graph of the Internet structure.

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