TY - GEN
T1 - Betweenness centrality in dense random geometric networks
AU - Kartun-Giles, Alexander P
AU - Georgiou, Orestis
AU - Dettmann, Carl P
PY - 2015/9
Y1 - 2015/9
N2 - 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 networks. In order to rank the importance of the network's communicating 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 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'.
AB - 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 networks. In order to rank the importance of the network's communicating 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 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'.
U2 - 10.1109/ICC.2015.7249352
DO - 10.1109/ICC.2015.7249352
M3 - Conference Contribution (Conference Proceeding)
SN - 9781467364300
T3 - IEEE International Conference on Communications
SP - 6450
EP - 6655
BT - ICC 2015 - 2015 IEEE International Conference on Communications
PB - Institute of Electrical and Electronics Engineers (IEEE)
T2 - IEEE International Conference on Communications, ICC 2015
Y2 - 8 June 2015 through 12 June 2015
ER -