### Abstract

We consider networks formed by the union of M random 1 -regular directed graphs. These graphs are also called permutation models in the literature. We first present a proof showing that the expansion factor of such graphs is greater than or equal to N a.a.s when M> 4\;\log\; N, where N is the number of nodes in the network. The reason for considering such random graph models is their applicability in the design of peer-to-peer networks and data center networks of switches. Assuming that each node in the network has upload and download capacities greater than 8\; \log\; N, we also show that the above result implies that all-to-all communication is possible in such a network, if the total incoming data rate and the total outgoing data rate at each node are both less than or equal to 1.

Original language | English (US) |
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Article number | 6971166 |

Pages (from-to) | 43-52 |

Number of pages | 10 |

Journal | IEEE Transactions on Network Science and Engineering |

Volume | 1 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2014 |

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science Applications
- Computer Networks and Communications

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## Cite this

*IEEE Transactions on Network Science and Engineering*,

*1*(1), 43-52. [6971166]. https://doi.org/10.1109/TNSE.2014.2376777