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The Infinite Locally Random Graph

Please always quote using this URN:urn:nbn:de:0296-matheon-2884
  • We investigate properties of a certain countably infinite graph called the infinite locally random graph, written R_N. The graph R_N arises in the study of models for massive, self-organizing networks like the web-graph. We characterize the isomorphism type of R_N as the limit of a random process, and via a domination elimination ordering. We prove that R_N satisfies vertex deletion properties generalizing inexhaustibility. As is the case for the infinite random graph R, R_N has a universal automorphism group and endomorphism monoid. Unlike R, R_N isometrically embeds all finite graphs.

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Metadaten
Author:Manuel Bodirsky, Anthony Bonato
URN:urn:nbn:de:0296-matheon-2884
Referee:Hans Jürgen Prömel
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2005/05/11
Release Date:2005/10/31
Preprint Number:269
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