Persistent homology for flow networks — track the birth and death of topological features as flow increases.

Pure Rust, zero dependencies. Builds Vietoris-Rips filtrations from distance matrices and computes persistence diagrams that reveal the topological structure of flow networks at every scale.

• Vietoris-Rips filtration — simplices appear as the distance threshold increases
• Persistence diagrams — birth/death pairs for 0-dimensional (components) and 1-dimensional (loops) features
• Betti numbers — count of topological features at each threshold
• Zero dependencies — all from scratch

A flow network has structure at multiple scales. At low flow, the network is fragmented — many isolated components. As flow increases, components merge, loops form, and the topology changes. Persistent homology tracks which features survive across scales and how long they persist.

A feature that's born early and dies late is a robust topological property. A feature that appears and immediately vanishes is noise.

use topological_flow::{rips_filtration, compute_persistence, PersistencePair};
// Distance matrix for 4 points
let dist = vec![
 vec![0.0, 1.0, 2.0, 3.0],
 vec![1.0, 0.0, 1.0, 2.0],
 vec![2.0, 1.0, 0.0, 1.0],
 vec![3.0, 2.0, 1.0, 0.0],
];
// Build filtration up to radius 3.0, allowing triangles
let filtration = rips_filtration(&dist, 2, 3.0);
// Compute persistence pairs
let pairs = compute_persistence(&filtration);
for pair in &pairs {
 println!("H{}: born at {:.2}, dies at {:.2} (persistence = {:.2})",
 pair.dim, pair.birth, pair.death, pair.persistence());
}

Part of the SuperInstance topological ecosystem:

• topology-lab — Interactive visualization of persistent homology
• wasserstein-narrative — Persistence diagrams for story analysis
• topological-flow — Persistence for flow networks (this repo)

cargo test

[dependencies]
topological-flow = { git = "https://github.com/SuperInstance/topological-flow" }

MIT

Part of the SuperInstance ecosystem.