Random geometric graphs with general connection functions

Carl P Dettmann, Orestis Georgiou

Research output: Contribution to journalArticle (Academic Journal)peer-review

38 Citations (Scopus)
346 Downloads (Pure)

Abstract

In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks “soft” or “probabilistic” connection models have recently been introduced, involving a “connection function” H(r) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.
Original languageEnglish
Article number032313
Number of pages14
JournalPhysical Review E
Volume93
Issue number3
Early online date14 Mar 2016
DOIs
Publication statusPublished - Mar 2016

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