Betweenness Centrality in Dense Random Geometric Networks
Abstract
Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how often all paths in the network characterisable as topologically `shortest' contain a given node (betweenness centrality), deriving an expression in terms of a known integral whenever 1) the network boundary is the perimeter of a disk and 2) the network is extremely dense. Our method shows how similar formulas can be obtained for any convex geometry. Numerical corroboration is provided, as well as a discussion of our formula's potential use for cluster head election and boundary detection in densely deployed wireless ad hoc networks.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.8521
 Bibcode:
 2014arXiv1410.8521K
 Keywords:

 Computer Science  Social and Information Networks;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Computational Geometry;
 Computer Science  Networking and Internet Architecture;
 Mathematics  Probability;
 Physics  Physics and Society
 EPrint:
 6 pages, 3 figures