### 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 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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

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

**Load distribution in weighted complex networks.** / Goh, Kwang-Il; Noh, J. D.; Kahng, B.; Kim, D.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 72, no. 1, 017102. https://doi.org/10.1103/PhysRevE.72.017102

}

TY - JOUR

T1 - Load distribution in weighted complex networks

AU - Goh, Kwang-Il

AU - Noh, J. D.

AU - Kahng, B.

AU - Kim, D.

PY - 2005/7/1

Y1 - 2005/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=27244447186&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27244447186&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.72.017102

DO - 10.1103/PhysRevE.72.017102

M3 - Article

VL - 72

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 1

M1 - 017102

ER -