On the Distribution of Random Geometric Graphs

Mihai Alin Badiu, Justin P. Coon

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5 Citationer (Scopus)
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Abstract

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random topology, properties (e.g., connectedness), or Shannon entropy as a measure of the graph’s topological uncertainty (or information content). Moreover, the distribution is also relevant for determining average network performance or designing protocols. However, a major impediment in deducing the graph distribution is that it requires the joint probability distribution of the n(n − 1)/2 distances between n nodes randomly distributed in a bounded domain. As no such result exists in the literature, we make progress by obtaining the joint distribution of the distances between three nodes confined in a disk in R2. This enables the calculation of the probability distribution and entropy of a three-node graph. For arbitrary n, we derive a series of upper bounds on the graph entropy; in particular, the bound involving the entropy of a three-node graph is tighter than the existing bound which assumes distances are independent. Finally, we provide numerical results on graph connectedness and the tightness of the derived entropy bounds.
OriginalsprogEngelsk
Titel2018 IEEE International Symposium on Information Theory, ISIT 2018
Antal sider5
ForlagIEEE
Publikationsdato2018
Sider2137-2141
Artikelnummer8437912
ISBN (Trykt)9781538647806
ISBN (Elektronisk)978-1-5386-4781-3
DOI
StatusUdgivet - 2018
Begivenhed 2018 IEEE International Symposium on Information Theory - Vail, USA
Varighed: 17 jun. 201822 jun. 2018

Konference

Konference 2018 IEEE International Symposium on Information Theory
Land/OmrådeUSA
ByVail
Periode17/06/201822/06/2018
NavnI E E E International Symposium on Information Theory. Proceedings
ISSN2157-8117

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