### Abstract

In this work we study the asymptotic traffic flow in Gromov hyperbolic graphs when the traffic decays exponentially with the distance. We prove that under general conditions, there exists a phase transition between local and global traffic. More specifically, assume that the traffic rate between two nodes u and v is given by R(u, v) ^{d(u, v)}, where d(u, v) is the distance between the nodes. Then there exists a constant _{c}, that depends on the geometry of the network, such that if 1 _{c} the traffic is global and there is a small set of highly congested nodes called the core. However, if _{c} then the traffic is essentially local and the core is empty which implies very small congestion.

Original language | English (US) |
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Title of host publication | 5th International Symposium on Communications Control and Signal Processing, ISCCSP 2012 |

DOIs | |

State | Published - Jul 27 2012 |

Event | 5th International Symposium on Communications Control and Signal Processing, ISCCSP 2012 - Rome, Italy Duration: May 2 2012 → May 4 2012 |

### Publication series

Name | 5th International Symposium on Communications Control and Signal Processing, ISCCSP 2012 |
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### Other

Other | 5th International Symposium on Communications Control and Signal Processing, ISCCSP 2012 |
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Country | Italy |

City | Rome |

Period | 5/2/12 → 5/4/12 |

### Keywords

- Complex Networks
- Congestion
- Hyperbolic Networks
- Spectral Gap
- Traffic Load

### ASJC Scopus subject areas

- Computer Networks and Communications
- Signal Processing

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## Cite this

*5th International Symposium on Communications Control and Signal Processing, ISCCSP 2012*[6217862] (5th International Symposium on Communications Control and Signal Processing, ISCCSP 2012). https://doi.org/10.1109/ISCCSP.2012.6217862