@MISC{Marinari06andrandom, author = {E. Marinari and R. Monasson and G. Semerjian}, title = {and random graphs.}, year = {2006} }

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Abstract

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. Introduction. An increasing amount of data has been collected on the topology of realworld networks appearing in many different contexts, the Internet being only one of many examples [1]. A natural line of research in this field consists in identifying characteristic features of the networks, to compare them with theoretical models and potentially disprove the latter. The simplest of these properties is the distribution of vertex degrees, which has