Weighted Rail Network Topological Analysis: Efficiency, Eccentricity, and Related Attributes

The North American railroad system can be well represented by a network with 302,943 links (track segments) and 250,388 nodes (stations, junctions, and waypoints), and other points of interest based on publicly accessible geographical information obtained from the Bureau of Transportation Statistics (BTS) and the Federal Railroad Administration (FRA). From this large network, a slightly more consolidated subnetwork representing the major freight railroads and Amtrak was selected for analysis. Recent improvements in network and graph theory and improvements in all-pairs shortest path algorithms make it more feasible to process certain characteristics on large networks with reduced computation time and resources. The characteristics of networks at issue in this study to support network-level risk and resilience studies include node efficiency, node eccentricity, and other attributes derived from those measures, such as network arithmetic efficiency, network geometric central node, radius, and diameter, and some distribution measures of the node characteristics. Rail distance weighting factors, representing the length of each rail derived from BTS data, are mapped to corresponding links and are used as link weights for the purpose of computing shortest paths and subsequent characteristics. These network characteristics can be used to place resources and plan for natural hazard and disaster scenarios. They relate to many practical applications such as network efficiency to distribute traffic and a network’s ability to recover from disruptions.