On the effect of very large nodes in Internet graphs

Hannu Reittu; Ilkka Norros

doi:10.1109/GLOCOM.2002.1189105

On the effect of very large nodes in Internet graphs

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

5 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 language	English
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)	978-0-7803-7632-8
DOIs	https://doi.org/10.1109/GLOCOM.2002.1189105
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
Country/Territory	Taiwan, Province of China
City	Taipei
Period	17/11/02 → 21/11/02

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10.1109/GLOCOM.2002.1189105

https://publications.vtt.fi/julkaisut/muut/2002/Reittu_Norros.pdf

Cite this

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title = "On the effect of very large nodes in Internet graphs",

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.",

author = "Hannu Reittu and Ilkka Norros",

note = "Project code: T1SU00227; IEEE Global Telecommunications Conference, Globecom 2002 ; Conference date: 17-11-2002 Through 21-11-2002",

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T1 - On the effect of very large nodes in Internet graphs

AU - Reittu, Hannu

AU - Norros, Ilkka

N1 - Project code: T1SU00227

PY - 2002

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N2 - 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.

AB - 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.

U2 - 10.1109/GLOCOM.2002.1189105

DO - 10.1109/GLOCOM.2002.1189105

M3 - Conference article in proceedings

SN - 978-0-7803-7632-8

VL - 3

SP - 2624

EP - 2628

BT - IEEE Global Telecommunications Conference, Globecom'02

PB - IEEE Institute of Electrical and Electronic Engineers

T2 - IEEE Global Telecommunications Conference, Globecom 2002

Y2 - 17 November 2002 through 21 November 2002

ER -

On the effect of very large nodes in Internet graphs

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