Size of the giant component in a random geometric graph
type: Item
instance of: scholarly article
title: Size of the giant component in a random geometric graph
zbMATH Open document ID: 1283.60017
DOI: 10.1214/12-AIHP498
author: Ghurumuruhan Ganesan
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2013-11-19T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aihp/1380718740
review text: A random geometric graph \(G\) is defined with \(n\) nodes that are independently selected according to a common probability distribution with density \(f\) in the unit square. Two nodes are joined by an edge if their distance is less than a specified positive value \(r=r(n)\). The density \(f\) is assumed to have its infimum and its supremum strictly between 0 and infinity. By dividing the unit square into subsquares, so that nodes in adjacent subsquares can be joined by an edge, a technique is developed to investigate the structure of the giant component for a certain range of values of \(r\). Size and diameter are estimated as \(n\) tends to infinity and \(r\) is proportional to the square root of \(1/n\) or of \((\log n)/n\). Both uniform and non-uniform \(f\) are considered.
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 05C80
zbMATH DE Number: 6229201
zbMATH Keywords: random geometric graph
zbMATH Keywords: size of giant component
zbMATH Keywords: number of components
zbMATH Keywords: graph diameter
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6229201