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

Illka Norros, Hannu Reittu

    Research output: Contribution to journalArticleScientificpeer-review

    5 Citations (Scopus)

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)251-266
    Number of pages16
    JournalInternet Mathematics
    Volume5
    Issue number3
    Publication statusPublished - 2008
    MoE publication typeA1 Journal article-refereed

    Fingerprint

    Infinite Variance
    Random Graphs
    Power Law
    Attack
    Giant Component
    Graph Model
    Shortest path
    Tail
    Siméon Denis Poisson
    Upper bound
    Graph in graph theory
    Vertex of a graph
    Resistance

    Cite this

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

    In: Internet Mathematics, Vol. 5, No. 3, 2008, p. 251-266.

    Research output: Contribution to journalArticleScientificpeer-review

    TY - JOUR

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    AU - Norros, Illka

    AU - Reittu, Hannu

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    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

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    EP - 266

    JO - Internet Mathematics

    JF - Internet Mathematics

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