A persistent homology model of street network connectivity

We 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.