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

Enzo Marinari, Remi Monasson, Guilhem Semerjian

Published 2005-07-22, updated 2006-01-03Version 2

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.