Pynauty can be used to compare graphs for isomorphism and to determine their automorphism group in a Python programming environment. Pynauty is a Python/C extension module using library components from the Nauty package by Brendan McKay.

Current version is distributed and has been tested with nauty2_8_8.

Here is an example of pynauty's usage in an interactive session.

>>> from pynauty import *
>>> g = Graph(5)
>>> g.connect_vertex(0, [1, 2, 3])
>>> g.connect_vertex(2, [1, 3, 4])
>>> g.connect_vertex(4, [3])
>>> print(g)
Graph(number_of_vertices=5, directed=False,
 adjacency_dict = {
  0: [1, 2, 3],
  2: [1, 3, 4],
  4: [3],
 },
 vertex_coloring = [
 ],
)
>>> autgrp(g)
([[3, 4, 2, 0, 1]], 2.0, 0, [0, 1, 2, 0, 1], 3)
>>> 
>>> g.connect_vertex(1, [3])
>>> autgrp(g)
([[0, 1, 3, 2, 4], [1, 0, 2, 3, 4]], 4.0, 0, [0, 0, 2, 2, 4], 3)
>>>
>>> g.set_vertex_coloring([set([3])])
>>> print(g)
Graph(number_of_vertices=5, directed=False,
 adjacency_dict = {
  0: [1, 2, 3],
  1: [3],
  2: [1, 3, 4],
  4: [3],
 },
 vertex_coloring = [
  set([3]),
  set([0, 1, 2, 4]),
 ],
)
>>> autgrp(g)
([[1, 0, 2, 3, 4]], 2.0, 0, [0, 0, 2, 3, 4], 4)
>>>

Please note that multigraphs are not supported, but this limitation can be worked around by encoding multigraphs as simple graphs. For details, see the documentation and Nauty's manual.

You can install pynauty using pip, just type

pip install --upgrade pynauty

Many binary wheels are provided for recent Linux and macOS systems. When your system is not compatible with any of the provided binary wheels pip attempts to build the wheel of the extension module in your local system. This happens automatically and the process is transparent to the user. For local builds pip expects that the required tools are available.

You can force the local (re)compilation during install by issuing

pip install --no-binary pynauty pynauty

Regardless of which way the installation was accomplished, afterwards you can test the result by running the provided tests.

python <path-to-installed-package>/pynauty/tests/test_minimal.py

If you have pytest installed then you can run the full test suit by issuing

pip install pytest
python -m pytest <path-to-installed-package>/pynauty

That takes a few seconds but then you can be sure in having a binary compatible module.

The pynauty package comes with an HTML documentation with examples. You can read it with your favorite browser:

<your-browser>  <path-to-installed-package>/pynauty/docs/html/index.html

Apart from Python the requirements are the same as for building Nauty.

• Python 3.8 - 3.12
• An ANSI C compiler
• GNU make

You can download the source distribution form PyPi by issuing:

pip download --no-binary pynauty pynauty

Please note, the source distribution also contains Nauty2_8_8's source.

If you really are interested in the low level details then unpack the downloaded source distribution, change into pynauty's directory and type make. The Makefile is self-documenting in the sense that invoking make without arguments will list all available targets with short explanations.

Questions, bug reports, pull requests, especially the ones extending the Python module's functionality, are welcome. Please, open an issue first to discuss what you would like to change.

Pull requests must be made on a dedicated topic-branch of your choice and not against upstream/main. Before submitting a pull request, make sure that your fork is up to date with upstream. Also update tests, documentation, examples as appropriate with the changes in your PR.

• @goens helped creating pytest components.

• Sam Morley-Short (@sammorley-short) added canon_label() function.

• Frank Bryce fixed the issue of misleadingly accepting multigraphs.

Pynauty is distributed under the terms of GPL v3 WITHOUT ANY WARRANTY. For the exact details on licensing see the file COPYING.

Please note, Nauty is covered by its own licensing terms. For the exact details see the file src/nauty2_8_8/COPYRIGHT.