An algorithm for counting circuits: application to real-world and random   graphs
  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. 
Enzo Marinari, Remi Monasson and Guilhem Semerjian