Skip to main content

ollivier_ricci_curvature

rust_igraph

Function ollivier_ricci_curvature 

Source 
pub fn ollivier_ricci_curvature(
    graph: &Graph,
    alpha: f64,
) -> IgraphResult<Vec<f64>>
Expand description

Ollivier-Ricci curvature for each edge (lazy random walk variant).

For an edge (u, v), defines probability measures on the neighborhoods: mu_u(w) = alpha if w == u, else (1-alpha) / deg(u) for each neighbor.

The Ollivier-Ricci curvature is kappa(u,v) = 1 - W1(mu_u, mu_v) / d(u,v). Since d(u,v) = 1 for adjacent vertices in unweighted graphs: kappa(u,v) = 1 - W1(mu_u, mu_v).

Uses an approximate Wasserstein computation via the ATD (Average Transportation Distance) heuristic for efficiency.

§Parameters

  • graph — Undirected, connected graph.
  • alpha — Laziness parameter in [0, 1). alpha = 0 gives the standard Ollivier-Ricci; alpha = 0.5 is the “Lin-Lu-Yau” variant.

§Examples

use rust_igraph::{Graph, ollivier_ricci_curvature};

// Triangle: high curvature (positive)
let g = Graph::from_edges(&[(0,1),(1,2),(0,2)], false, Some(3)).unwrap();
let curv = ollivier_ricci_curvature(&g, 0.0).unwrap();
assert!(curv[0] > 0.0);