The Mathematics of Spatial Configuration: Revisiting, Revising and Critiquing Justified Plan Graph Theory

TLDR: The justified plan graph (JPG) was the first practical analytical method developed as part of the theory of Space Syntax, which purported to provide a graphical, mathematical and associated theoretical model for analysing the spatial configuration of buildings.

Abstract: The justified plan graph (JPG) was the first practical analytical method developed as part of the theory of Space Syntax, which purported to provide a graphical, mathematical and associated theoretical model for analysing the spatial configuration of buildings. In spite of early interest, in recent years relatively little research using this method has been published, perhaps because the JPG method is rarely explained in its totality and when it is, the descriptions are often inconsistent or unclear. Although it is now embedded in several software programs and its use may be more widespread, it is no better understood and after processing there is a marked lack of consistency in how the results are interpreted. This paper provides a historical background for the development of the JPG and a discussion of its conceptual or theoretical origins, followed by a “worked example” of the mathematics of the JPG. In combination with the results for two further cases, the paper identifies some important interpretative limits in the method and uses the examples to explain its potential use in design analysis. Finally, the paper discusses how the consistent application of this method to sets of related buildings is likely to produce a more valuable, and statistically viable, basis for future work.