### Abstract

*N*has a giant component that is supersmall in the sense that the typical distance between vertices is of order log log

*N*. The shortest paths travel through a core consisting of nodes with high mean degrees. In this paper we derive upper bounds for the distance between two random vertices when an upper part of the core is removed, including the case that the whole core is removed.

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

Pages (from-to) | 251-266 |

Number of pages | 16 |

Journal | Internet Mathematics |

Volume | 5 |

Issue number | 3 |

Publication status | Published - 2008 |

MoE publication type | A1 Journal article-refereed |

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### Cite this

*Internet Mathematics*,

*5*(3), 251-266.

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*Internet Mathematics*, vol. 5, no. 3, pp. 251-266.

**Attack resistance of power-law random graphs in the finite-mean, infinite-variance region.** / Norros, Illka; Reittu, Hannu.

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

TY - JOUR

T1 - Attack resistance of power-law random graphs in the finite-mean, infinite-variance region

AU - Norros, Illka

AU - Reittu, Hannu

PY - 2008

Y1 - 2008

N2 - We consider a conditionally Poisson random-graph model in which the mean degrees, “capacities,” follow a power-tail distribution with finite mean and infinite variance. Such a graph of size N has a giant component that is supersmall in the sense that the typical distance between vertices is of order log log N. The shortest paths travel through a core consisting of nodes with high mean degrees. In this paper we derive upper bounds for the distance between two random vertices when an upper part of the core is removed, including the case that the whole core is removed.

AB - We consider a conditionally Poisson random-graph model in which the mean degrees, “capacities,” follow a power-tail distribution with finite mean and infinite variance. Such a graph of size N has a giant component that is supersmall in the sense that the typical distance between vertices is of order log log N. The shortest paths travel through a core consisting of nodes with high mean degrees. In this paper we derive upper bounds for the distance between two random vertices when an upper part of the core is removed, including the case that the whole core is removed.

M3 - Article

VL - 5

SP - 251

EP - 266

JO - Internet Mathematics

JF - Internet Mathematics

SN - 1542-7951

IS - 3

ER -