Part VI: Network Analysis
Street networks as mathematical graphs — spectral properties, diffusion, accessibility, and resilience through percolation theory. Extracting actionable insight from real city topology.
Part Overview
Street networks as mathematical graphs — spectral properties, diffusion, accessibility, and resilience through percolation theory. OSMnx extracts real city data, the graph Laplacian and its Fiedler value reveal connectivity structure, heat diffusion quantifies accessibility via effective resistance, and the Molloy-Reed criterion predicts the percolation threshold for network collapse.
Key Topics
- • OSMnx real city data
- • Graph Laplacian
- • Fiedler value
- • Heat diffusion on networks
- • Effective resistance
- • Percolation threshold
- • Molloy-Reed criterion
3 chapters | Graph theory meets urban form | From streets to spectra
Chapters
Chapter 1: Street Networks (OSMnx)
Downloading, cleaning, and analyzing real street networks with OSMnx. Graph representations of urban topology, degree distributions, centrality measures, and basic network statistics for real cities.
Chapter 2: Spectral Analysis
The graph Laplacian and its spectrum encode network structure. The Fiedler value (algebraic connectivity) measures bottlenecks, heat diffusion quantifies accessibility, and effective resistance gives a distance metric respecting all paths.
Chapter 3: Percolation Threshold
Network resilience through percolation theory. Random vs targeted node removal, the giant component transition, and the Molloy-Reed criterion for predicting when a street network fragments.