canonaut (Python)

Graph canonicalization and automorphism groups: Python bindings for canonaut, a safe Rust port of nauty. The PyPI package and the Rust crate share the name.

Install

pip install canonaut

Usage

Nodes can be any hashable value — ints, strings, tuples, whatever you already have. No need to relabel your graph to 0..n-1 first.

import canonaut

# Canonize a 4-cycle with arbitrary node labels
r = canonaut.canonize([("a","b"), ("b","c"), ("c","d"), ("d","a")])
print(r.num_orbits)          # 1  (vertex-transitive)
print(r.group_size1, r.group_size2)  # |Aut| ~= group_size1 * 10**group_size2
print(r.canonical_edges)     # edges of the canonical form (0..n-1 index space)

# Vertex colors (partition): vertices with different colors are never mapped
# onto each other by any automorphism, and the canonical form respects it.
r = canonaut.canonize(
    [(0,1), (1,2), (2,3)],
    colors={0: "red", 1: "red", 2: "blue", 3: "blue"},
)
print(r.num_orbits)          # 4 (colors broke the path's end-to-end symmetry)

# Automorphism generators, as {node: image_node} maps
r = canonaut.canonize([("a","b"),("b","c"),("c","d"),("d","a")], generators=True)
print(r.generators)

# Orbits, grouped by original node label
print(r.orbits)               # [['a','b','c','d']] for the 4-cycle

# Isomorphism test — works with different label sets on each side
canonaut.are_isomorphic(
    [("p","q"),("q","r"),("r","s"),("s","p")],
    [(1,2),(2,3),(3,4),(4,1)],
)  # True

# Hashable canonical key for deduplication — equal iff the graphs are isomorphic
key = r.canonical_bytes()

# networkx graphs work directly (duck-typed, no hard dependency)
import networkx as nx
r = canonaut.canonize(nx.petersen_graph())

Isolated vertices

nodes= includes vertices with no edges at all:

canonaut.canonize([("a","b")], nodes=["a", "b", "isolated"])

Directed graphs

canonaut.canonize(edges, directed=True)

Detected automatically for graph-like objects exposing .is_directed() (e.g. networkx.DiGraph).

Low-level API

canonaut.raw exposes the compiled extension directly: 0..n-1 integer vertex indices only, no node-label translation. Use it if you already have integer-labeled graphs and want to skip that overhead:

r = canonaut.raw.canonize(4, [(0,1),(1,2),(2,3)], colors=[0,0,1,1])

CanonResult

Attribute Type Meaning
labeling list Original nodes in canonical order — labeling[i] is the node placed at canonical position i
orbits list[list] Automorphism-group orbits, as groups of original nodes
canonical_edges list[tuple[int,int]] Edges of the canonical form, in canonical-position (0..n-1) space
group_size1, group_size2 float, int |Aut(G)| ~= group_size1 * 10**group_size2
num_orbits, num_generators int
generators list[dict] Automorphism generators as {node: image_node} maps (only when generators=True)
.canonical_bytes() bytes Hashable canonical key

Project links

Data verified by PyPI on Aug 12, 2026
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GitHub Statistics

Data verified by PyPI on Aug 12, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License

Apache Software License (Apache-2.0)

Requires

Python >=3.9

Tags

graph canonicalization automorphism isomorphism nauty

Classifiers

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