### Abstract

In scale-free networks, the degree distribution follows a power law with the exponent γ. Many model networks exist which reproduce the scale-free nature of the real-world networks. In most of these models, the value of γ is continuously tunable, thus is not universal. We study a problem of data packet transport in scale-free networks and define load at each vertex as the accumulated total number of data packets passing through that vertex when every pair of vertices send and receive a data packet along the shortest paths. We find that the load distribution follows a power law with an exponent δ for scale-free networks. Moreover, the load exponent δ is insensitive to the details of the networks in the range 2< γ ≤3. For the class of networks considered in this work, δ ≈ 2.2(1). We conjecture that the load exponent is a universal quantity to characterize and classify scale-free networks.

Original language | English |
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Pages (from-to) | 72-79 |

Number of pages | 8 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 318 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2003 Feb 1 |

Externally published | Yes |

### Keywords

- Load distributions
- Scale-free networks

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

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## Cite this

*Physica A: Statistical Mechanics and its Applications*,

*318*(1-2), 72-79. https://doi.org/10.1016/S0378-4371(02)01407-3