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Efficiency of star-like graphs and the Atlanta subway network

Author

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  • Ek, Bryan
  • VerSchneider, Caitlin
  • Narayan, Darren A.

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.

Suggested Citation

  • Ek, Bryan & VerSchneider, Caitlin & Narayan, Darren A., 2013. "Efficiency of star-like graphs and the Atlanta subway network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5481-5489.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:21:p:5481-5489
    DOI: 10.1016/j.physa.2013.06.055
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    References listed on IDEAS

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    1. Latora, Vito & Marchiori, Massimo, 2002. "Is the Boston subway a small-world network?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 109-113.
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