This repository collects research prototypes for studying urban form with topological data analysis, persistent homology, graph kernels, and street-network analysis. Most folders are self-contained case studies with their own notebooks, data, figures, and local README files.
The common theme is to represent cities or street networks as geometric, topological, or graph objects, then compare how urban connectivity, accessibility, morphology, and service coverage change under different filtrations or graph-similarity methods.
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15_min_city_ph/: proof of concept for studying 15-minute-city accessibility in Medellin with persistent homology. The main workflow builds a walking-time accessibility surface to shopping malls and retail buildings, converts it into a cubical-complex filtration, and studies connected accessibility islands and persistent service voids. The folder includes the main mall-accessibility notebook, exploratory service-query notebooks, cached walking-time data, a Medellin GraphML network, and exported figures. -
edge_importance_ph/: persistent-homology experiments based on road importance. This project computes edge-importance proxies such as edge betweenness centrality, uses those scores to define filtrations of road networks, and studies how connectivity and cycles evolve as less important roads are added. It also includes Corcoran-and-Jones-style road-hierarchy replication work, executable filtration pipelines, comparison-city graph exports, experiment outputs, and Medellin road-importance figures. -
elevation_filtration_ph/: experiments on how city connectedness changes under elevation and street-slope filtrations. The notebooks download or load OSMnx street networks, enrich them with elevation data, and build sublevel or superlevel filtrations by node elevation or edge slope. The folder contains GraphML inputs for cities such as Medellin, Manizales, La Paz, Chicago, Lisbon, and Funchal, plus generated figures for slope and elevation experiments. -
graph_kernels/: graph-comparison experiments around Metric Graph Kernels via the Tropical Torelli Map, following Cao and Monod. The folder contains the kernel implementation, graph dataset preparation utilities, toy graph notebooks, MUTAG benchmark tests, city-classification replication notebooks, Boston-specific urban-pattern experiments, GraKeL tutorials, and synthetic grid/non-grid classification tests. -
levelset_urban_ph/: level-set persistent-homology experiments for urban street-network morphology. The pipeline rasterizes street networks or polygon samples, initializes a signed-distance field, propagates a level-set front through open space, computes cubical persistent homology, and exports persistence diagrams, barcodes, and landscapes. The folder also contains clustering and classification notebooks using Wasserstein distances and persistence landscapes, processed outputs for Medellin and U.S. city samples, and labeled input geometries.
Each top-level project folder is organized around some combination of:
- notebooks for exploratory analysis and reproducible case studies;
src/orpipeline/folders for reusable implementation code;data/,labeled_data/, orprocessed_data/folders for inputs and derived outputs;figs/orfigures/folders for exported plots, maps, persistence diagrams, and filtration snapshots;cache/,osmnx_cache/, and__pycache__/folders for generated intermediate files.
The folder-level README files provide more specific notes about methods, notebooks, and outputs inside each project.
All code is licensed under the MIT License, and the content is licensed under the Creative Commons Attribution License.
The content in this repository is licensed under the Creative Commons Attribution 4.0 International License, and the accompanying source code is licensed under the MIT License.