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

    Fingerprint

    Dive into the research topics of 'Distance graphs: from random geometric graphs to Bernoulli graphs and between'. Together they form a unique fingerprint.

    Cite this