### Abstract

*N*nodes are drawn independently from a distribution with a Pareto tail with index

*τ*∈(2,3) (finite mean and infinite variance), and the connections are then made randomly. We show that, asymptotically almost surely, the graph has a giant component, and the distance between two randomly selected nodes of the giant component is of the order log log

*N*. This high connectivity is a consequence of the spontaneous emergence of a “core network” consisting of nodes with high degrees. Our result sheds light on the structure of the random graph model and raises interesting issues on its similarities and dissimilarities with the real Internet.

Original language | English |
---|---|

Pages (from-to) | 3 - 23 |

Number of pages | 21 |

Journal | Performance Evaluation |

Volume | 55 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2004 |

MoE publication type | A1 Journal article-refereed |

### Fingerprint

### Keywords

- power law
- data networks
- internet
- stochastic models
- random graph model

### Cite this

*Performance Evaluation*,

*55*(1-2), 3 - 23. https://doi.org/10.1016/S0166-5316(03)00097-X

}

*Performance Evaluation*, vol. 55, no. 1-2, pp. 3 - 23. https://doi.org/10.1016/S0166-5316(03)00097-X

**On the power-law random graph model of massive data networks.** / Reittu, Hannu; Norros, Ilkka (Corresponding Author).

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - On the power-law random graph model of massive data networks

AU - Reittu, Hannu

AU - Norros, Ilkka

PY - 2004

Y1 - 2004

N2 - Simplifying stochastic models of the topology of Internet have been studied intensively during the past few years. One of the most interesting ones is a random graph, where the degrees of the N nodes are drawn independently from a distribution with a Pareto tail with index τ∈(2,3) (finite mean and infinite variance), and the connections are then made randomly. We show that, asymptotically almost surely, the graph has a giant component, and the distance between two randomly selected nodes of the giant component is of the order log log N. This high connectivity is a consequence of the spontaneous emergence of a “core network” consisting of nodes with high degrees. Our result sheds light on the structure of the random graph model and raises interesting issues on its similarities and dissimilarities with the real Internet.

AB - Simplifying stochastic models of the topology of Internet have been studied intensively during the past few years. One of the most interesting ones is a random graph, where the degrees of the N nodes are drawn independently from a distribution with a Pareto tail with index τ∈(2,3) (finite mean and infinite variance), and the connections are then made randomly. We show that, asymptotically almost surely, the graph has a giant component, and the distance between two randomly selected nodes of the giant component is of the order log log N. This high connectivity is a consequence of the spontaneous emergence of a “core network” consisting of nodes with high degrees. Our result sheds light on the structure of the random graph model and raises interesting issues on its similarities and dissimilarities with the real Internet.

KW - power law

KW - data networks

KW - internet

KW - stochastic models

KW - random graph model

U2 - 10.1016/S0166-5316(03)00097-X

DO - 10.1016/S0166-5316(03)00097-X

M3 - Article

VL - 55

SP - 3

EP - 23

JO - Performance Evaluation

JF - Performance Evaluation

SN - 0166-5316

IS - 1-2

ER -