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.

6 pages, 3 figures

References in corpus (2)

• Full Connectivity: Corners, edges and faces
• Impact of boundaries on fully connected random geometric networks

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