Distance graphs: from random geometric graphs to Bernoulli graphs and between

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

9 Scopus citations

Abstract

We introduce and study random distance graph. A random distance, D(n,g) results from placing n points uniformly at random on the unit area disk and connecting every two points independently with probability g(d), where d is the distance between the nodes and g is the connection function. We give a connection function g(r,a,d) with parameters r and a and show the following: (a) D(n,g(r,a)) captures as special cases both the standard random geometric graph G(n,r) and the Bernoulli random graph B(n,p) (a.k.a. Erdos-Renyi graph). (b) Using results from continuum percolation we are able to bound the connectivity threshold of D(n,g(r,a)), with G(n,r) and B(n,p) as special (previously known) cases. (c) Contrary to G(n,r) and B(n,p), for a wide range of r and α a is, in fact, a "Small World" graph with high clustering coefficient of about 0.5865a and diameter of ({log n}/{log log n}). As opposed to previous Small World models that rely on deterministic sub-structures to grantee connectivity, random distance graphs offer a completely randomized model with a proved bounds for connectivity threshold, clustering coefficient and diameter.

Original languageEnglish
Title of host publicationDIALM-POMC'08
Subtitle of host publicationProceedings of the ACM 5th International Workshop on Foundations of Mobile Computing
Pages71-77
Number of pages7
DOIs
StatePublished - 1 Dec 2008
Event5th ACM SIGACT-SIGOPS International Workshop on Foundations of Mobile Computing, DIALM-POMC - Toronto, ON, Canada
Duration: 22 Aug 200822 Aug 2008

Publication series

NameDIALM-POMC'08: Proceedings of the ACM 5th International Workshop on Foundations of Mobile Computing

Conference

Conference5th ACM SIGACT-SIGOPS International Workshop on Foundations of Mobile Computing, DIALM-POMC
Country/TerritoryCanada
CityToronto, ON
Period22/08/0822/08/08

Keywords

  • Bernoulli graphs
  • Connectivity
  • Distance graphs
  • Random geometric graphs
  • Small world

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Software

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