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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.
Original language | English |
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Title of host publication | 2018 IEEE International Symposium on Information Theory, ISIT 2018 |
Number of pages | 5 |
Publisher | IEEE |
Publication date | 2018 |
Pages | 2137-2141 |
Article number | 8437912 |
ISBN (Print) | 9781538647806 |
ISBN (Electronic) | 978-1-5386-4781-3 |
DOIs | |
Publication status | Published - 2018 |
Event | 2018 IEEE International Symposium on Information Theory - Vail, United States Duration: 17 Jun 2018 → 22 Jun 2018 |
Conference
Conference | 2018 IEEE International Symposium on Information Theory |
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Country/Territory | United States |
City | Vail |
Period | 17/06/2018 → 22/06/2018 |
Series | I E E E International Symposium on Information Theory. Proceedings |
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ISSN | 2157-8117 |
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Dive into the research topics of 'On the Distribution of Random Geometric Graphs'. Together they form a unique fingerprint.Projects
- 1 Finished
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Managing Interference in Dense Wireless Networks: An Approach Inspired by the Physics of Large Systems
Badiu, M. A.
01/03/2016 → 28/02/2018
Project: Research