graph-canon

Super fast and barebones graph canonicalization using nauty C-lib and built on petgraph.

Usage

Hashable Labels

If you are just looking to create a hashable object to determine isomorphism then it is simples to use the CanonLabeling struct.

This can be created from a Graph object directly.

Directed Graphs

use petgraph::{Directed, Graph};
use graph_canon::CanonLabeling;

let e1 = vec![(0, 1), (0, 2), (1, 2)]; // Isomorphic
let e2 = vec![(1, 0), (1, 2), (0, 2)]; // Isomorphic
let e3 = vec![(1, 0), (1, 2), (2, 1)]; // Non-Isomorphic

let g1 = Graph::<(), (), Directed>::from_edges(&e1);
let g2 = Graph::<(), (), Directed>::from_edges(&e2);
let g3 = Graph::<(), (), Directed>::from_edges(&e3);

let l1 = CanonLabeling::new(&g1);
let l2 = CanonLabeling::new(&g2);
let l3 = CanonLabeling::new(&g3);

assert_eq!(l1, l2);
assert_ne!(l1, l3);

Undirected Graphs

use petgraph::{Undirected, Graph};
use graph_canon::CanonLabeling;

let e1 = vec![(0, 1), (0, 2), (1, 2)]; // Isomorphic
let e2 = vec![(1, 0), (1, 2), (0, 2)]; // Isomorphic
let e3 = vec![(1, 0), (1, 2)];         // Non-Isomorphic

let g1 = Graph::<(), (), Undirected>::from_edges(&e1);
let g2 = Graph::<(), (), Undirected>::from_edges(&e2);
let g3 = Graph::<(), (), Undirected>::from_edges(&e3);

let l1 = CanonLabeling::new(&g1);
let l2 = CanonLabeling::new(&g2);
let l3 = CanonLabeling::new(&g3);

assert_eq!(l1, l2);
assert_ne!(l1, l3);

Recovering the Canonical Graph

If instead you are interested in working with the graph itself, you can use the canonize function to return a new Graph object

use petgraph::{Directed, Graph};
use graph_canon::canonize;

let edges = vec![(0, 1), (0, 2), (1, 2)];
let graph = Graph::<(), (), Directed>::from_edges(&edges);
let canon = canonize(&graph);
assert_eq!(canon.edge_count(), 3);

Timing Comparison

This crate is inspired by nauty-pet but is much faster as it is much simpler. (tests measured with criterion)

This test is using a randomly generated graph of 10 nodes and 0.5 probability of edge connection using random_gpn_graph

graph-canon             time:   [1.3272 µs 1.3276 µs 1.3285 µs]
Found 14 outliers among 100 measurements (14.00%)
  3 (3.00%) high mild
  11 (11.00%) high severe

nauty-pet               time:   [6.2591 µs 6.2738 µs 6.2956 µs]
Found 10 outliers among 100 measurements (10.00%)
  2 (2.00%) low mild
  4 (4.00%) high mild
  4 (4.00%) high severe