Efficiency of star-like graphs and the Atlanta subway network

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.