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

Enzo Marinari·Remi Monasson·Guilhem Semerjian
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Abstract

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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Enzo Marinari, Remi Monasson, Guilhem Semerjian. 2006-01-03. An algorithm for counting circuits: application to real-world and random graphs. https://doi.org/10.1209/epl%2Fi2005-10355-0

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