Path Diagrams: configurational descriptions from gis data, an Algorithm and its implications

Paper in proceeding, 2019

This paper proposes and explains a type of diagrams which share some of the characteristics distinctive of axial maps, while also differing substantially in some other aspects. A main discussion in Space Syntax is the capacity of different diagrammatic representations to describe relevant morphological characteristics of space: convex maps or visibility graphs at the scale of buildings; axial maps and other topological representations of streets or roads at urban and geographic scales. The relevance of these representations is often assessed through the correlation of the different metrics they afford with empirical observations of real phenomena, such as the flow, circulation and presence of people in space. This has led to an instrumentalist understanding of representations and models through their capacity to produce measurements that may be empirically correlated, relegating other aspects to a secondary plane. In their “Space Syntax” paper from 1976, Hillier et al. outlined a research programme based on the proposition of morphic languages and their syntaxes; the collection of maps and diagrams proposed by Hillier and Hanson years later in “the Social Logic of Space,” including the axial map, carried further this programme of a science of diagrams and “morphic languages,” rather than one focused on metrics and their empirical correlations. This paper wants to reconsider some of these original characteristics of the representations of spatial configurations, through the proposition of a diagram and an algorithm to generate it. This diagram has been developed for its use in the comparison and classification of spatial configurations. Using data available from Open Street Map, the algorithm presented here builds a graph in which its vertices consist of straight paths on the original graph, and edges represent crossings or adjacencies of these straight paths. The process involves the implicit construction of what is known in graph theory as the line graph and a set of operations so as to derive the final graph from it. This graph is referred to in the paper as the “straight path graph,” as it consists of paths, both in their graph theoretical sense of a sequence of non-repeated vertices, and in their more general sense as circulation paths on a map. The insistence on its qualities as a diagram is the result of a need to describe more concisely spatial organisations in order to map, compare and classify them, either by hand or through the use of diverse automatic techniques and algorithms, rather than its use in the production and correlation of metrics with empirical observations.