Efficiency of star-like graphs and the Atlanta subway network |
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Authors: | Bryan Ek Caitlin VerSchneider Darren A Narayan |
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Institution: | 1. School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, United States;2. Mathematics Department, Nazareth College, Rochester, NY 14618, United States |
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Abstract: | The distance d(i,j) between any two vertices i and j in a graph is the number of edges in a shortest path between i and j. If there is no path connecting i and j, then d(i,j)=∞. In 2001, Latora and Marchiori introduced the measure of efficiency between vertices in a graph (Latora and Marchiori, 2001) 1]. The efficiency between two vertices i and j is defined to be ∈i,j=j. In this paper, we investigate the efficiency of star-like networks, and show that networks of this type have a high level of efficiency. We apply these ideas to an analysis of the Metropolitan Atlanta Rapid Transit Authority (MARTA) Subway system, and show this network is 82% as efficient as a network where there is a direct line between every pair of stations. |
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Keywords: | Efficiency Graphs Networks Star-like graphs MARTA Subway network |
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