Monte Carlo tests of small-world architecture for coarse-grained networks of the United States railroad and highway transportation systems

• We use Monte Carlo randomizations to test US transportation infrastructure data for small-worldness.
• We compare the US railroad network, US highway network, and a simple planar network.
• Transportation networks have small-world architecture relative to global randomizations.
• Transportation networks do not have small-world architecture relative to planar randomizations.
• The small-world structure of transportation networks owes more to their planarity than to the topology of transportation links.

Several studies have shown that human transportation networks exhibit small-world structure, meaning they have high local clustering and are easily traversed. However, some have concluded this without statistical evaluations, and others have compared observed structure to globally random rather than planar models. Here, we use Monte Carlo randomizations to test US transportation infrastructure data for small-worldness. Coarse-grained network models were generated from GIS data wherein nodes represent the 3105 contiguous US counties and weighted edges represent the number of highway or railroad links between counties; thus, we focus on linkage topologies and not geodesic distances. We compared railroad and highway transportation networks with a simple planar network based on county edge-sharing, and with networks that were globally randomized and those that were randomized while preserving their planarity. We conclude that terrestrial transportation networks have small-world architecture, as it is classically defined relative to global randomizations. However, this topological structure is sufficiently explained by the planarity of the graphs, and in fact the topological patterns established by the transportation links actually serve to reduce the amount of small-world structure.