### Abstract

We study the load distribution in weighted networks by measuring the effective number of optimal paths passing through a given vertex. The optimal path, along which the total cost is minimum, crucially depends on the cost distribution function pc(c). In the strong disorder limit, where pc(c)∼c-1, the load distribution follows a power law both in the Erdos-Rényi (ER) random graphs and in the scale-free (SF) networks, and its characteristics are determined by the structure of the minimum spanning tree. The distribution of loads at vertices with a given vertex degree also follows the SF nature similar to the whole load distribution, implying that the global transport property is not correlated to the local structural information. Finally, we measure the effect of disorder by the correlation coefficient between vertex degree and load, finding that it is larger for ER networks than for SF networks.

Original language | English |
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Article number | 017102 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 72 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2005 Jul |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*72*(1), [017102]. https://doi.org/10.1103/PhysRevE.72.017102