Topological Analytics of Large North American Railroad Networks: Length-Weighted Average Distance, Eccentricity, and Related Attributes

Network metrics are proposed for determining and comparing the average distance and eccentricity of large topological networks through the application of shortest path algorithms, such as for a large railroad network with hundreds of thousands of nodes and hundreds of thousands of links, for estimating such attributes for North American railroad networks, and comparatively examining by key operators. The network chosen for this demonstration is a detailed geometric mapping of the North American railroad system from a publicly available data set. Challenges for the computation of large-network characteristics involve maintaining acceptable complexity levels for the computation of all characteristics due to the relatively large network size while maintaining the feasibility of practical applications and performing all computations on consumer-available hardware within a reasonable computation time of hours or less. The railroad network characteristics computed herein may be useful to railroad stakeholders for planning efficient network extensions, quantifying resilience, identifying risk enhancements or weaknesses, or general network design purposes, particularly with meaningful data used as weights for links. Network characteristics are computed for subsections of the railroad network as subnetworks including Amtrak and the largest railroads operators in North America and are used as case studies to illustrate the information derived from the network analysis. Additionally, the methods and tools are applicable to any other large networks and other related data structures such as trees to similarly characterize them beyond what is typically inferred from most basic analyses.