Figure 5

Filtered minimum-route paths more accurately capture how a container can move through the network based on liner shipping service routes. Path and route length statistics differ substantially between the filtered minimum-route paths (blue circles) and shortest paths through all of the path graph (orange crosses), the directed co-route graph (green stars), and the undirected co-route graph (purple triangles). Each panel shows a normalized histogram with an unnormalized version in the inset plot. Network path lengths (a): Minimum-route paths are much longer (mean 20 edges) than the shortest paths through the undirected (3.5) or directed (3.5) co-route graph and the path graph (mean 5.4). The mean shipping distance (b) for the minimum-route paths (mean 21,861.3 km) is shorter than that of the undirected (22,784.05) and directed (22,767.85) co-route graphs, but distribution for the minimum-route paths has a longer tail. The minimum-route paths are longer than shortest paths through the path graph, both in terms of mean (19,532.4) and maximum distance. The number of routes required (c) for the filtered paths (mean 3.2 routes) is shorter than in the path graph (4.7), where each shortest path may use a different number of routes. Only 0.3% of the shortest paths through the undirected and 0.4% of paths through the directed co-route graph are viable based on the shipping routes, but those that do correspond to viable paths use the minimum number of routes (means 2.6 and 2.7, respectively). Finally, the number of paths per pair of ports (d) is reduced substantially in the path graph and filtered minimum-route paths