An algorithm for counting circuits: application to real-world and random graphs
arXiv:cond-mat/0507525 · doi:10.1209/epl/i2005-10355-0
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.
7 pages, 3 figures, minor corrections, accepted version