should be no direct AB link because these points should be connected via C or F. The same process is repeated taking point B as a vantage point, such that if the algorithm finds either AB or BA intercepted by other route-efficient points, this link is dropped from the undirected graph. Figure 11 shows the thus generated US-grade hypothetical network connecting the 453 (port-)cities. It has 1459 edges, some of which intersect and should be broken up further.

<!-- Start of picture text --> Figure 11: Demonstration of Network Finding Algorithm<br>543 (Port-)City Sizes (Population) US-Grade Hypothetical Network<br><!-- End of picture text --> _Notes:_ The LHS shows the 453 (port-)cities; circles reflect population. The RHS shows the result of applying the network finding algorithm described above, requiring US route efficiency of 0.834 (Wolfram, 2021) and a maximum 20<sup>_◦_</sup> deviation.

To propose optimal network extensions, I apply the algorithm to a complete transport network graph where all 1379 nodes are fully connected. Using the US network efficiency and 20<sup>_◦_</sup> angle criterion as illustrated above yields a staggering 2,031 new edges, shown in Appendix Figure A8. Since this is close to the number of existing edges, and many of the new links overlap, I adjust the parameters of the algorithm to generate fewer potential links. Concretely, I increase the maximum angle for intercepting nodes to _α_ = 45<sup>_◦_</sup> , and use the European route efficiency estimate of 0.767 by Wolfram (2021), which is lower than the US value of 0.843 partly due to Europe’s more fragmented (water-bound) geography. In addition, I let OSRM compute a full road distance matrix between all 1,379 nodes and remove connections that already have a route efficiency of 2/3 or higher. The 516 links retained by this modified algorithm, if straight, thus reduce travel distance by _≥_ 50%.

I then verify whether these links can be constructed and remove 46 links significantly intercepted by waterbodies or protected areas. Some proposed links across the closed Morocco-Algeria border already exist. I keep them and reduce their construction costs in the network optimization process. Finally, I manually add 11 links that I consider important for improved transport flow. In total, I retain 481 new links. Figure 12 draws them as thin green lines. Exempting one crossing in northern Mali, where adding a node would add no value for routing purposes, and a similar case in central Kenya, these links don’t intersect and thus imply no additional nodes to the graph.

In reality, roads constructed along these links will not be perfectly straight. I assume that new links have the same average route efficiency as existing links, which is 0.83.<sup>20</sup> Thus, I divide the spherical distance spanned by new links by 0.83 to estimate their road distance (edge weight), yielding 104,000km in total. In the remainder of this paper, I show simplified graphs with straight edges in all smaller plots to make them more legible. All computations, however, use edge weights corresponding to actual road distances and travel times, with existing network as in Figure 12.

> 20The route efficiency across individual links of 0.83 is larger than the overall network route efficiency of 0.68 because the latter considers full trans-African routes comprising multiple links.

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