Distortion Induced by Planarization in Urban Road Networks: An Empirical Assessment Using Edge-Betweenness-Prioritized Sub-graphs Across 40 Cities

Urban road networks are routinely represented as planar graphs even though overpasses, underpasses, and multi-level interchanges create crossings that no planar embedding can preserve. This study quantifies the distortion introduced by this representational choice across 40 cities. An edge-betweenness-prioritized greedy procedure extracts a maximal planar sub-graph from each network, which is then compared across six metrics. Average shortest-path cost increased in every city, whereas the diameter was unchanged in more than half the sample. The magnitude of distortion scaled with the proportion of edges the planarity constraint excluded, but was unrelated to baseline network scale. Planarization, therefore, requires context-specific assessment.