| Summary: | Road hierarchy and network structure are intimately linked; however, there is not a consistent basis for representing and analyzing the particular hierarchical nature of road network structure. This paper introduces the line structure—identified mathematically as a kind of linearly ordered incidence structure—as a means of representing road network structure and demonstrates its relation to existing representations of road networks: the “primal” graph, the “dual” graph, and the route structure. In doing so, the paper shows how properties of continuity, junction type, and hierarchy relating to differential continuity and termination are necessarily absent from primal and dual graph representations but intrinsically present in line structure representations. A new property indicative of hierarchical status—“cardinality”—is introduced and illustrated with application to example networks. The paper concludes by highlighting newly explicit relationships between different kinds of road network structure representation.
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