Abstract
AbstractWe propose a novel model of street network connectivity which uses a method from the field of applied topology called “persistent homology”. The output from this model is a pair of density functions which model the relative strength and frequency of connected components and cycles in the network. In this context, strength is a function of street type, such as motorway or residential, with more significant street types providing greater connectivity. The pair of density functions output from the model are easily interpreted and provide novel insights into the connectivity properties of different street networks. We demonstrate the usefulness of this model through an analysis of UK and US city street networks. This analysis identifies tangible similarities and differences in the connectivity of different cities plus ways in which the connectivity of individual cities might be improved.
Highlights
Cities are important phenomena in our society
In this article we propose a novel model of street network connectivity based on persistent homology
As described in the introduction to this article, we propose a novel model of street network connectivity where connectivity is modelled in terms of the relative strength and frequency of connected components and cycles
Summary
Cities are important phenomena in our society. Currently more than half of the world’s population live in urban areas, with this percentage projected to grow to two-thirds by 2050 (Ritchie, 2018). These persistence diagrams are transformed into a corresponding pair of density functions which can be interpreted This contrasts with existing models of street network connectivity, reviewed, which output a single value indicating the level of connectivity. As stated in the motivation at the beginning of this section, we wish to model street network connectivity in terms of connected components and cycles while considering that more significant streets provide a greater level of connectivity We achieve this by computing the persistent homology of the filtration described in the previous subsection. Since larger cities will have graph representations with a greater number of edges, their corresponding persistence diagrams will have a correspondingly greater number of elements with significant persistence This in turn results in a bias where cities with similar sized street networks are determined to be more similar. TA B L E 2 The 40 US Metropolitan Statistical Areas considered plus the number of vertices (|V|) and edges (|E|) in the corresponding graph representations
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