Dual Graph
A method in space syntax that considers edges as nodes and nodes as edges. In urban street networks, large avenues made of several segments become single nodes while intersections with other avenues or streets become links (edges). This method is particularly useful to reveal hierarchical structures in a planar network. Based on a planar network such as urban streets (A), space syntax proposes to consider line segments differently from traditional graph theory, where links (edges) are streets and intersections are nodes (vertices). The axial map (B) first defines the line segments based on their continuity (e.g. based on names of avenues and boulevards, or other qualitative criterion). The dual graph (C) represents those segments as nodes and their intersections as links. It allows for discovering hidden structural properties of planar networks such as the hierarchy of arteries and the true connectivity of the network.