gravel-fragility 2.2.1

Fast road network fragility analysis with contraction hierarchies

Gravel

Fast road network fragility analysis at scale.

Gravel is a C++ library (with Python bindings) for computing how vulnerable road networks are to edge failures. Given a graph, it answers questions like:

• "How isolated does this location become when 10% of its roads fail?"
• "Which counties are most dependent on a single critical route?"
• "What's the composite fragility score for every US county?"

The library is built around contraction hierarchies for fast shortest-path queries, and a Dijkstra + incremental SSSP pipeline for edge-removal analysis. On a 200K-node county graph, it computes isolation fragility in ~2 seconds.

Installation

conda (recommended for C++ dependencies)

conda install -c conda-forge gravel-fragility

pip (source build — requires C++ compiler)

pip install gravel-fragility

For OSM data loading, install libosmium separately (brew install libosmium on macOS, apt install libosmium2-dev on Debian/Ubuntu).

From source

git clone https://github.com/rhoekstr/gravel.git
cd gravel
cmake -B build -DGRAVEL_BUILD_PYTHON=ON -DGRAVEL_USE_OSMIUM=ON
cmake --build build -j

Quick Start

Python

import gravel

# Load a road network (from OSM PBF)
graph = gravel.load_osm_graph("county.osm.pbf", gravel.SpeedProfile.car())

# Build contraction hierarchy (one-time cost)
ch = gravel.build_ch(graph)

# Compute isolation fragility for a location
cfg = gravel.LocationFragilityConfig()
cfg.center = gravel.Coord(35.43, -83.45)  # Bryson City, NC
cfg.radius_meters = 30000  # 30km
cfg.monte_carlo_runs = 20

result = gravel.location_fragility(graph, ch, cfg)
print(f"Isolation risk: {result.isolation_risk:.3f}")
print(f"Reachable nodes: {result.reachable_nodes}")
print(f"Directional coverage: {result.directional_coverage:.2f}")

C++

#include <gravel/gravel.h>

auto graph = gravel::load_osm_graph({"county.osm.pbf", gravel::SpeedProfile::car()});
auto ch = gravel::build_ch(*graph);

gravel::LocationFragilityConfig cfg;
cfg.center = {35.43, -83.45};
cfg.radius_meters = 30000;
cfg.monte_carlo_runs = 20;

auto result = gravel::location_fragility(*graph, ch, cfg);
std::cout << "Isolation risk: " << result.isolation_risk << "\n";

Key Features

Sub-library architecture

Six independent libraries with a strict dependency DAG — link only what you need:

Library	Purpose	Dependencies
gravel-core	Graph representation, basic routing	stdlib, OpenMP
gravel-ch	Contraction hierarchy + blocked queries	gravel-core
gravel-simplify	Graph simplification, bridges	+ gravel-ch
gravel-fragility	All fragility analysis (Eigen/Spectra)	+ gravel-simplify
gravel-geo	OSM loading, regions, snapping (libosmium)	+ gravel-simplify
gravel-us	US TIGER/Census specializations	+ gravel-geo

Analysis modules

• Route fragility — per-edge replacement path analysis
• Location fragility — isolation risk for a geographic point (new Dijkstra+IncrementalSSSP)
• County fragility — composite index combining bridges, connectivity, accessibility, fragility
• Scenario fragility — event-conditional analysis (hazard footprints)
• Progressive elimination — degradation curve with Monte Carlo / greedy strategies
• Tiled analysis — spatial fragility fields for visualization
• Region assignment — node-to-polygon mapping (point-in-polygon)
• Graph coarsening — collapse regions into meta-nodes

Performance

Measured on an Apple M-series laptop (see bench/baselines/routing_performance.md):

Operation	200K-node graph (Swain Co.)	593K-node graph (Buncombe Co.)
OSM PBF load	0.36s	0.99s
CH build	0.85s	3.92s
CH distance query	3.8 µs	8.8 µs
CH route (with path unpacking)	82.7 µs	144.8 µs
Distance matrix cell (OpenMP)	5.5 µs	6.3 µs
Route fragility (per path edge)	~60 ms	~124 ms
Location fragility (MC=20)	2.1 s	~8 s

At-scale benchmarks:

• National per-county isolation fragility (3,221 counties): 3.1 hours
• National inter-county fragility (8,547 adjacent pairs incl. cross-state): ~22 hours

Documentation

• REFERENCE.md — complete API reference (all functions, all types)
• docs/PRD.md — product requirements and architecture
• docs/ — full documentation site (also on GitHub Pages)
• examples/ — Python notebooks and C++ sample programs

Example: National US County Analysis

# Run fragility analysis on all ~3,221 US counties
python scripts/national_fragility.py --output-dir output/

# Results are in output/county_isolation_fragility.csv
# Visualize with:
python scripts/visualize_results.py

Sample findings from the national run (April 2026):

Most vulnerable states	Mean risk
New Hampshire	0.638
Maine	0.571
Rhode Island	0.570
Connecticut	0.563

Most resilient states	Mean risk
Kansas	0.146
Nebraska	0.162
Iowa	0.163
North Dakota	0.165

The Great Plains grid-states score lowest — flat land with rectangular road networks have extensive redundancy. Mountain and coastal states score highest — constrained geography forces single-path corridors.

Requirements

Runtime:

• C++20 compiler (GCC 11+, Clang 14+, MSVC 2022+)
• CMake 3.20+
• Python 3.10+ (for bindings)

Optional:

• libosmium (for OSM PBF loading)
• Apache Arrow (for Parquet output)

Bundled (via CMake FetchContent):

• pybind11
• Eigen + Spectra
• nlohmann/json
• Catch2 (tests)

Contributing

See CONTRIBUTING.md. Bug reports and feature requests welcome via GitHub Issues.

License

Apache 2.0 — see LICENSE. Free for commercial and research use.

Citation

If you use Gravel in academic work, please cite:

@software{gravel2026,
  author = {Hoekstra, Robert},
  title = {Gravel: Fast Road Network Fragility Analysis},
  year = {2026},
  url = {https://github.com/rhoekstr/gravel},
  version = {2.2.0}
}

About the Author

Built by Robert Hoekstra — more projects and writing at awrylabs.com.