On the effect of very large nodes in Internet graphs

Hannu Reittu, Ilkka Norros

    Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

    4 Citations (Scopus)


    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 languageEnglish
    Title of host publicationIEEE Global Telecommunications Conference, Globecom'02
    PublisherIEEE Institute of Electrical and Electronic Engineers
    ISBN (Print)978-0-7803-7632-8
    Publication statusPublished - 2002
    MoE publication typeA4 Article in a conference publication
    EventIEEE Global Telecommunications Conference, Globecom 2002 - Taipei, Taiwan, Province of China
    Duration: 17 Nov 200221 Nov 2002


    ConferenceIEEE Global Telecommunications Conference, Globecom 2002
    Country/TerritoryTaiwan, Province of China


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