## Abstract

We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-Rényi networks, based on recursion equations for the shells around a reference node and for the paths originating from it. The results are in agreement with numerical simulations for a broad range of network sizes and connectivities. The average and standard deviation of the distribution are also obtained. In the case in which the mean degree scales as N^{α} with the network size, the distribution becomes extremely narrow in the asymptotic limit, namely almost all pairs of nodes are equidistant, at distance d = [1/α] from each other. The distribution of shortest path lengths between nodes of degree m and the rest of the network is calculated. Its average is shown to be a monotonically decreasing function of m, providing an interesting relation between a local property and a global property of the network. The methodology presented here can be applied to more general classes of networks.

Original language | American English |
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Article number | 26006 |

Journal | Lettere Al Nuovo Cimento |

Volume | 111 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jul 2015 |

### Bibliographical note

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