Line graphs e contrazioni: un approccio rigoroso alla space syntax

TL;DR

This paper introduces a rigorous approach to space syntax using line graphs and contractions, enabling flexible analysis of urban environments and applications like noise mapping.

Contribution

It presents a novel method combining line graph algorithms and contractions to generalize space syntax analysis beyond traditional axial line methods.

Findings

The method can reproduce traditional axial line results.

It allows analysis of various urban quantities such as noise.

The approach is implemented in Mathematica for practical use.

Abstract

The methods of the space syntax have been the subject of extensive discussion, and several techniques to identify the axis lines have been proposed. The space syntax can be represented in terms of line graph, a graphs defined on the edge of a given primary graph. By means of the line graph algorithms, a system of labels defined on the edges of the primary graph is transformed into a system of labels on the vertices of the line graph. The contraction of adjacent edges with the same label allows to build a more general graph than those generated with the methods of the space syntax. By means of the functions implemented in Mathematica is therefore possible to redefine the space syntax on any system of urban quantities (labels) and reproduce the results of the axial lines as a special case. As an example is discussed a possible application of the method to the urban noise analysis.