Betweenness Centrality in Dense Random Geometric Networks

Alexander P. Kartun-Giles; Orestis Georgiou; Carl P. Dettmann

doi:10.1109/icc.2015.7249352

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arXiv · 1410.8521

Betweenness Centrality in Dense Random Geometric Networks

Alexander P. Kartun-Giles·Orestis Georgiou·Carl P. Dettmann

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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.

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cs.SI cond-mat.stat-mech cs.CG cs.NI math.PR physics.soc-ph

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Alexander P. Kartun-Giles, Orestis Georgiou, Carl P. Dettmann. 2016-10-26. Betweenness Centrality in Dense Random Geometric Networks. https://doi.org/10.1109/icc.2015.7249352

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