Figure 7

Longer routes use more edges on average, but all routes are not used to the same extent, and not all appearances are equal. Panel (a) shows the length of a shipping service route (horizontal axis) against the number of unique route sequences that route appears in (# Sequences, blue triangles), and the total number of edges from that route used across all minimum-route paths (Total Edges, orange stars). Longer service routes tend to be more highly weighted, but some shorter routes are also prevalent in realizing minimum-route paths. Panel (b) shows the average number of edges used per appearance in a route sequence for each service route (Total Edges divided by # Sequences). The length of a route is a natural limit on the number of edges that can be used from that route in a given path; if the points were to fall along the line \(y=x\), then each time a route appeared in a route sequence we could expect most or all of its edges to be used in that minimum-route path. On average roughly half of the edges from a route are used whenever it appears in a route sequence (\(R^{2}=0.92\)). Panel (c) shows a direct relationship (in logarithmic space) between the number of sequences a route appears in and the total edges used from the route, while (d) shows the same quantities but with the y-axis scaled to show the proportion of the maximum possible edges. Values near the bottom indicate that few edges from a route were used with respect to the number of times the route appeared and its length, while high values indicate that each time the route is used all of its edges appear