### Abstract

We analyse a random graph where the node degrees are (almost) independent and have a distribution with finite mean but infinite variance - a region observed in empirical studies of the Internet. We show that the existence of very large nodes has a great influence on the connectivity. If N denotes the number of nodes it seems that the distance between two randomly chosen nodes of the giant component grows as slowly as log log(N). The essential observation is that very large nodes form a spontaneously arising "core network", which plays a crucial role in the connectivity, although its proportional size goes to zero as N → ∞. Several results related to the core are proven rigorously, and a sketch of a full proof is given. Some simulations providing illustration of the findings are presented. Consequences of the results are discussed.

Original language | English |
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Title of host publication | IEEE Global Telecommunications Conference, Globecom'02 |

Publisher | IEEE Institute of Electrical and Electronic Engineers |

Pages | 2624-2628 |

Volume | 3 |

ISBN (Print) | 0-7803-7632-3 |

DOIs | |

Publication status | Published - 2002 |

MoE publication type | A4 Article in a conference publication |

Event | IEEE Global Telecommunications Conference, Globecom 2002 - Taipei, Taiwan, Province of China Duration: 17 Nov 2002 → 21 Nov 2002 |

### Conference

Conference | IEEE Global Telecommunications Conference, Globecom 2002 |
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Country | Taiwan, Province of China |

City | Taipei |

Period | 17/11/02 → 21/11/02 |

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## Cite this

Reittu, H., & Norros, I. (2002). On the effect of very large nodes in Internet graphs. In

*IEEE Global Telecommunications Conference, Globecom'02*(Vol. 3, pp. 2624-2628). IEEE Institute of Electrical and Electronic Engineers. https://doi.org/10.1109/GLOCOM.2002.1189105