Distribution of shortest cycle lengths in random networks

Abstract

We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to configuration model networks, for which analytical results for the DSPL were obtained before. We first calculate the fraction of nodes in the network which reside on at least one cycle. Conditioning on being on a cycle, we provide the DSCL over ensembles of configuration model networks with degree distributions which follow a Poisson distribution (Erdos-Rényi network), degenerate distribution (random regular graph) and a power-law distribution (scale-free network). The mean and variance of the DSCL are calculated. The analytical results are found to be in very good agreement with the results of computer simulations.

44 pages, 11 figures

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Cited by in corpus (4)

• Analytical results for the distribution of first hitting times of random walks on random regular graphs
• Statistical analysis of edges and bredges in configuration model networks
• Towards the cycle structures in complex network: A new perspective
• The distribution of shortest path lengths on trees of a given size in subcritical Erdos-Renyi networks