## canonical-form

Reduce graphs and other combinatorial structures modulo isomorphism

### 12 releases (breaking)

 0.9.4 Sep 6, 2020 Oct 23, 2019 Oct 20, 2019 Jun 26, 2019 Jan 22, 2019

#14 in Visualization

Used in flag-algebra

36KB
645 lines

# canonical-form

Algorithm to reduce combinatorial structures modulo isomorphism.

This can typically be used to to test if two graphs are isomorphic.

The algorithm manipulates its input as a black box by the action of permutations and by testing equallity with element of its orbit, plus some user-defined functions that help to break symmetries.

``````use canonical_form::Canonize;

// Simple Graph implementation as adjacency lists
#[derive(Ord, PartialOrd, PartialEq, Eq, Clone, Debug)]
struct Graph {
}

impl Graph {
fn new(n: usize, edges: &[(usize, usize)]) -> Self {
let mut adj = vec![Vec::new(); n];
for &(u, v) in edges {
}
for list in &mut adj {
list.sort() // Necessary to make the derived `==` correct
}
}
}

// The Canonize trait allows to use the canonial form algorithms
impl Canonize for Graph {
fn size(&self) -> usize {
}
fn apply_morphism(&self, perm: &[usize]) -> Self {
let mut adj = vec![Vec::new(); self.size()];
for (i, nbrs) in self.adj.iter().enumerate() {
}
}
fn invariant_neighborhood(&self, u: usize) -> Vec<Vec<usize>> {
}
}

// Usage of library functions
// Two isomorphic graphs
let c5 = Graph::new(5, &[(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]);
let other_c5 = Graph::new(5, &[(0, 2), (2, 1), (1, 4), (4, 3), (3, 0)]);
assert_eq!(c5.canonical(), other_c5.canonical());

// Non-isomorphic graphs
let p5 = Graph::new(5, &[(0, 1), (1, 2), (2, 3), (3, 4)]);
assert!(c5.canonical() != p5.canonical());

// Recovering the permutation that gives the canonical form
let p = c5.morphism_to_canonical();
assert_eq!(c5.apply_morphism(&p), c5.canonical());

// Enumerating automorphisms
assert_eq!(c5.canonical().automorphisms().count(), 10)
``````