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.
The algorithm in REF is an approximation algorithm that has proven its efficiency in estimating large number of cycles in polynomial time when applied to real world networks.
An algorithm for counting circuits : application to real-world and random graphs
EPL
Physics Mathematics