Syntactic Step Depth

Step depth is the raw count of topological moves between two spaces, and mean depth is the average of that count from one space to all others. Integration is mean depth normalised so it can be compared across spaces and across systems of different sizes: mean depth is converted to relative asymmetry and then to real relative asymmetry, whose reciprocal is integration. In short, step depth is the basic ingredient and integration is the standardised, comparable measure of how central or accessible a space is within the configuration.

Space syntax argues that much of how people perceive, navigate and use space depends on configuration — how spaces connect and how many transitions separate them — rather than on exact metres. Counting topological steps captures this relational structure and, empirically, integration computed from step depth predicts movement and land-use patterns very well. That said, modern practice often complements topological depth with angular and metric measures, since gradient, distance and travel time clearly matter too.

Step depth is the foundational calculation of space syntax. From it come mean depth, relative asymmetry and integration, which are the standard configurational measures applied to axial maps, segment maps and convex maps of buildings and cities. The broader space-syntax method adds related measures such as connectivity, choice (betweenness) and angular segment analysis, plus visibility-based tools like isovists and visibility graph analysis, but they all build on or sit alongside the depth-based core introduced by Hillier and Hanson.