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Topological properties of the one dimensional exponential random geometric graph
Author(s) -
Gupta Bhupendra,
Iyer Srikanth K.,
Manjunath D.
Publication year - 2008
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20174
Subject(s) - exponential random graph models , random geometric graph , random graph , mathematics , exponential distribution , exponential function , geometric graph theory , graph , struct , voltage graph , discrete mathematics , combinatorics , line graph , computer science , mathematical analysis , statistics , programming language
In this article we study the one‐dimensional random geometric (random interval) graph when the location of the nodes are independent and exponentially distributed. We derive exact results and limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008