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Intersecting
geodesics and centrality in graphs
Emily Carter, Bryan Ek, Danielle Gonzalez, Rigoberto Flórez and Darren A. Narayan
Vol. 12 (2019), No. 1, 31–43
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Abstract |
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In a graph, vertices that are more central are often placed at the intersection of geodesics between other pairs of vertices. This model can be applied to organizational networks, where we assume the flow of information follows shortest paths of communication and there is a required action (i.e., signature or approval) by each person located on these paths. The number of actions a person must perform is linked to both the topology of the network as well as their location within it. The number of expected actions that a person must perform can be quantified by betweenness centrality. The betweenness centrality of a vertex is the ratio of shortest paths between all other pairs of vertices and in which appears to the total number of shortest paths from to . We precisely compute the betweenness centrality for vertices in several families of graphs motivated by different organizational networks. |
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Keywords
betweenness centrality, shortest paths, distance
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Mathematical Subject Classification 2010
Primary: 05C12, 05C82
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Milestones
Received: 4 March 2017
Revised: 26 July 2017
Accepted: 20 January 2018
Published: 31 May 2018
Communicated by Kenneth S. Berenhaut
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Authors |
| Emily Carter | |
| School of Mathematical
Sciences Rochester Institute of Technology Rochester, NY United States |
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| Bryan Ek | |
| Department of Mathematics Rutgers University Piscataway, NJ United States |
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| Danielle Gonzalez | |
| Department of Software
Engineering Rochester Institute of Technology Rochester, NY United States |
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| Rigoberto Flórez | |
| Department of Mathematics and
Computer Science The Citadel Charleston, SC United States |
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| Darren A. Narayan | |
| School of Mathematical
Sciences Rochester Institute of Technology Rochester, NY United States |
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