Betweenness Centrality in Dense Random Geometric Networks
Alexander P. Kartun-Giles, Orestis Georgiou, Carl P. Dettmann · 2016
Abstract—Random geometric networks are mathematical structures consisting of a set of nodes placed randomly within a bounded set V ⊆ Rd mutually coupled with a probability dependent on their Euclidean separation, and are the classic model used within the expanding field of ad-hoc wireless net-works. In order to rank the importance of network nodes, we consider the well established ‘betweenness ’ centrality measure (quantifying how often a node is on a shortest path of links between any pair of nodes), providing an analytic treatment of betweenness within a random graph model using a continuum approach by deriving a closed form expression for the expected betweenness of a node placed within a dense random geometric network formed inside a disk of radius R. We confirm this with numerical simulations, and discuss the importance of the formula for mitigating the ‘boundary effect ’ connectivity phenomenon, for cluster head node election protocol design and for detecting the location of a network’s ‘vulnerability backbone’. I.