Applying Depth Decay Functions to Space Syntax Network Graphs 089

Core to the mathematical innovations of space syntax is the concept of graph-radius. In this paper, the authors propose a new mathematical mechanism to provide a relative measure for the local/global configuration of an axial line. We propose that cumulative depth be redefined as CD = Sum (1/((di-1)^k)) where d is the depth from node i to the origin and k is a constant factor. This method is based on the requirement that all nodes, within a graph must be included in the analysis. As a result of this stipulation, there is no need to relativize the results of a given axial map according to the total number of its axial lines (or nodes in its graph). The authors then demonstrate that larger factors of k are equivalent to smaller radii in standard integration calculations. By using different values of k such as 0 and negative values the authors go on to show that a number of different measures can be approximated by simple changes in the k factor. The authors conclude their paper by correlating standard ‘radii measures’ (at different radii) and the newly proposed ‘decay measures’ (for different values of k) results for a number of axial maps and hence clearly demonstrating that this mechanism produces strongly correlated results and that the concept of radius, as used in space syntax, may be unified with other space syntax measures, harmonising them within a single family of equations. This paper concludes that ‘radius’ may be replaced by a decay function applied to the network graph and identifies some optimal decay functions.