settlement layer illustrating the spatial distribution of 8 pixel classifications: water, very low density (rural), low density, rural cluster, suburban or per-urban, semi-dense urban cluster, dense urban cluster, and urban cluster.

# Road network model

We extract road networks from the OSM data set using convex hulls created from settlement cluster boundaries as spatial masks. OSM provides a free, openly licensed, volunteer-contributed repository of geographic information with a focus on streets and roads. As of August 2021, approximately 7.9 million contributors had created this database with more than 796 million roads, coastlines, administrative boundaries, and other linear features known as “ways”<sup>70</sup> . Barrington-Leigh et al.<sup>71</sup> assessed the completeness of OSM road network data in countries around the world as of 2017. They found that globally, OSM is 83% complete, and more than 40% of countries–including several in the developing world–have a fully mapped street network<sup>4</sup> . However, there still exists a significant discrepancy in the completeness of road networks—countries with good internet access tend to be more complete. The completeness of the OSM road network has a U-shaped relationship with population density—smaller towns and villages with medium population density are likely to have missing roads<sup>71</sup> .

In addition, past studies<sup>71–73</sup> revealed relatively lower levels of completeness in road networks that are lower in the road hierarchy such as tertiary and residential roads. Such discrepancy will introduce selection bias which could potentially invalidate the subsequent travel simulations in this study. To address this issue, we first extract all drivable roads<sup>5</sup> from the OSM data set for all clusters at the global scale and then evaluate the relative completeness of tertiary and residential roads based on the extracted road network. For each settlement cluster, we compare road network density (total road length divided by the area of the cluster’s convex hull, unit: km/sqkm) between two types of road network: a) drivable road network excluding tertiary and residential road types and b) tertiary and residential road networks only.

We evaluate the percentile rank of network density for both types among all clusters as well as the percentile ratio–the quotient of road network density percentile rank (tertiary and residential roads excluded) and its tertiary and residential network density percentile rank) (Fig. 3a). Percentile rank measures the percentage of network density values in the frequency distribution that are equal to or lower than it. For example, if a cluster’s tertiary and residential road network density is greater than 50% of the densities of all clusters, then it is at the 50<sup>th</sup> percentile, where 50 is the percentile rank. A higher percentile rank suggests higher network density relative to other settlement clusters. Percentile ratio measures the inequality between the two network types aforementioned based on the distribution of network densities. A percentile ratio of 1 suggests no difference between the percentile ranks of the two network types. A percentile ratio greater than 1 suggests that the percentile rank of road network density excluding tertiary and residential roads is higher than that of tertiary and residential roads alone. This translates to the potential of insufficient

> 4 It should be noted that only roads with the following tags in the OSM road database were included in the completeness evaluation study: “motorway”, “motorway_link”, “trunk”, “trunk_link”, “primary”, “primary_link”, “secondary”, “secondary_link”, “tertiary”, “residential”, “road”, “unclassified”, and “living_street”.

> 5 OSM uses a “key-value” framework for data labeling and organization. The highway key/tag is the primary tag used for any kind of street or way. To extract, download and create graphs for road networks for each settlement cluster, we use the graph module of OSMnx specifying the network type parameter as “drive_service”. The built-in query within the graph module under this specification returns all roads with the “highway” key/tag and further filters out roads with the following values: “abandoned”, “bridleway”, “bus_guideway”, “construction”, “corridor”, “cycleway”, “elevator”, “escalator”, “footway”, “path”, “pedestrian”, “planned”, “platform”, “proposed”, “raceway”, “service”, “steps”, “track”, and any roads with “no motor” specification.

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