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

3 Citations (Scopus)

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 languageEnglish
Title of host publicationIEEE Global Telecommunications Conference, Globecom'02
PublisherIEEE Institute of Electrical and Electronic Engineers
Pages2624-2628
Volume3
ISBN (Print)0-7803-7632-3
DOIs
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

Conference

ConferenceIEEE Global Telecommunications Conference, Globecom 2002
CountryTaiwan, Province of China
CityTaipei
Period17/11/0221/11/02

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    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