passagemath-graphs 10.8.1
passagemath: Graphs, posets, hypergraphs, designs, abstract complexes, combinatorial polyhedra, abelian sandpiles, quivers
Requires Python: <3.15,>=3.11

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 passagemath: Graphs, posets, hypergraphs, designs, abstract complexes, combinatorial polyhedra, abelian sandpiles, quivers
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`passagemath <https://github.com/passagemath/passagemath>`__ is open
source mathematical software in Python, released under the GNU General
Public Licence GPLv2+.

It is a fork of `SageMath <https://www.sagemath.org/>`__, which has been
developed 2005-2026 under the motto “Creating a Viable Open Source
Alternative to Magma, Maple, Mathematica, and MATLAB”.

The passagemath fork uses the motto "Creating a Free Passage Between the
Scientific Python Ecosystem and Mathematical Software Communities."
It was created in October 2024 with the following goals:

-  providing modularized installation with pip from binary wheels,
   - this major project was started in May 2020 in the Sage codebase and completed in passagemath 10.5.29 (May 2025),

-  establishing first-class membership in the scientific Python
   ecosystem,

-  giving `clear attribution of upstream
   projects <https://groups.google.com/g/sage-devel/c/6HO1HEtL1Fs/m/G002rPGpAAAJ>`__,

-  providing independently usable Python interfaces to upstream
   libraries,

-  offering `platform portability and integration testing
   services <https://github.com/passagemath/passagemath/issues/704>`__
   to upstream projects,

-  inviting collaborations with upstream projects,

-  `building a professional, respectful, inclusive
   community <https://groups.google.com/g/sage-devel/c/xBzaINHWwUQ>`__,

-  `empowering Sage users to participate in the scientific Python ecosystem
   <https://github.com/passagemath/passagemath/issues/248>`__ by publishing packages,

-  developing a port to WebAssembly (`Pyodide <https://pyodide.org/en/stable/>`__, emscripten-forge) for
   serverless deployment with Javascript,

-  developing a native Windows port
   - passagemath 10.6.1 (July 2025) published the first pip-installable wheel packages for native Windows on x86_64,
   - passagemath packages became available in the [MSYS2 software distribution](https://packages.msys2.org/search?t=pkg&q=passagemath) in November 2025.

Moreover, the passagemath project:

-  provides a stable, frequently updated version of the Sage distribution,
-  integrates additional mathematical software, notably Macaulay2, a full set of GAP packages,
   and the Combinatorial Matrix Recognition library,
-  curates a library of Sage user packages.

`Full documentation <https://passagemath.org/docs/latest/html/en/index.html>`__ is
available online.

passagemath attempts to support and provides binary wheels suitable for
all major Linux distributions and recent versions of macOS.

Binary wheels for native Windows (x86_64, ARM) are are available for a subset of
the passagemath distributions. Use of the full functionality of passagemath
on Windows currently requires the use of Windows Subsystem for Linux (WSL)
or virtualization.

The supported Python versions in the passagemath-10.8.x series are 3.11.x-3.14.x;
the passagemath-10.6.x series (EOL 2026-10) still supports Python 3.10.x.


About this pip-installable distribution package
-----------------------------------------------

This pip-installable package ``passagemath-graphs`` is a distribution of a part of the Sage Library.  It provides a small subset of the modules of the Sage library ("sagelib", ``passagemath-standard``) for computations with graphs, posets, complexes, etc.

It consists of over 170 first-party Python and Cython modules and uses the `Boost Graph Library <https://github.com/boostorg/graph>`_, with additional functionality from `NetworkX <https://networkx.github.io/>`_ and several other libraries.


What is included
----------------

* `Graph Theory <https://passagemath.org/docs/latest/html/en/reference/graphs/index.html>`_

* `Trees <https://passagemath.org/docs/latest/html/en/reference/combinat/sage/combinat/enumerated_sets.html#trees>`_

* `Posets <https://passagemath.org/docs/latest/html/en/reference/combinat/sage/combinat/posets/all.html>`_

* `Abstract Complexes <https://passagemath.org/docs/latest/html/en/reference/topology/index.html>`_

* `Combinatorial Designs and Incidence Structure <https://passagemath.org/docs/latest/html/en/reference/combinat/sage/combinat/designs/all.html>`_

* `Finite State Machines, Automata, Transducers <https://passagemath.org/docs/latest/html/en/reference/combinat/sage/combinat/finite_state_machine.html>`_

* `Cluster Algebras and Quivers <https://passagemath.org/docs/latest/html/en/reference/combinat/sage/combinat/cluster_algebra_quiver/all.html>`_

* `Knot Theory <https://passagemath.org/docs/latest/html/en/reference/knots/index.html>`_

* `Sandpiles <https://passagemath.org/docs/latest/html/en/reference/dynamics/sage/sandpiles/sandpile.html>`_

* see https://github.com/passagemath/passagemath/blob/main/pkgs/sagemath-graphs/MANIFEST.in


Examples
--------

A quick way to try it out interactively::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-graphs[test]" ipython
    In [1]: from passagemath_graphs import *

    In [6]: g = Graph([(1, 3), (3, 8), (5, 2)]); g
    Out[6]: Graph on 5 vertices

    In [7]: g.is_connected()
    Out[7]: False


Available as extras, from other distributions
---------------------------------------------

Libraries
~~~~~~~~~

``pip install passagemath-graphs[benzene,buckygen,plantri]`` additionally make
various graph generators available via `passagemath-benzene <https://pypi.org/project/passagemath-benzene/>`_, `passagemath-buckygen <https://pypi.org/project/passagemath-buckygen/>`_, and `passagemath-plantri <https://pypi.org/project/passagemath-plantri/>`_.

``pip install passagemath-graphs[bliss]`` additionally installs `passagemath-bliss <https://pypi.org/project/passagemath-bliss/>`_ for the purpose
of computing graph (iso/auto)morphisms.

``pip install passagemath-graphs[cliquer]`` additionally installs `passagemath-cliquer <https://pypi.org/project/passagemath-cliquer/>`_

``pip install passagemath-graphs[cmr]`` additionally installs `passagemath-cmr <https://pypi.org/project/passagemath-cmr/>`_ for recognition and decomposition algorithms
for network matrices, totally unimodular matrices and regular matroids, series-parallel matroids, etc.

``pip install passagemath-graphs[gap]`` additionally installs `passagemath-gap <https://pypi.org/project/passagemath-gap/>`_ for group-theoretic functionality.

``pip install passagemath-graphs[igraph]`` additionally installs
`igraph <https://python.igraph.org/en/stable/>`_::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-graphs[igraph,test]" ipython
    In [1]: from passagemath_graphs import *

    In [2]: ## Example depending on igraph goes here

``pip install passagemath-graphs[mcqd]`` additionally installs `passagemath-mcqd <https://pypi.org/project/passagemath-mcqd/>`_

``pip install passagemath-graphs[nauty]`` additionally installs `passagemath-nauty <https://pypi.org/project/passagemath-nauty/>`_ for computing
automorphism groups of graphs and digraphs.

``pip install passagemath-graphs[networkx]`` additionally installs
`NetworkX <https://networkx.github.io>`__::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-graphs[networkx,test]" ipython
    In [1]: from passagemath_graphs import *

    In [2]: ## Example depending on networkx goes here

``pip install passagemath-graphs[pari]`` additionally installs `passagemath-pari <https://pypi.org/project/passagemath-pari/>`_

``pip install passagemath-graphs[planarity]`` additionally installs `passagemath-planarity <https://pypi.org/project/passagemath-planarity/>`_ for planarity testing.

``pip install passagemath-graphs[rankwidth]`` additionally installs `passagemath-rankwidth <https://pypi.org/project/passagemath-rankwidth/>`_ for rank width and rank decompositions.

``pip install passagemath-graphs[tdlib]`` additionally installs `passagemath-tdlib <https://pypi.org/project/passagemath-tdlib/>`_ for computing tree decompositions.


Features
~~~~~~~~

``pip install passagemath-graphs[combinat]`` additionally installs `passagemath-combinat <https://pypi.org/project/passagemath-combinat/>`_

``pip install passagemath-graphs[editor]`` additionally installs the interactive graph editor `phitigra <https://pypi.org/project/phitigra/>`_.

``pip install passagemath-graphs[groups]`` additionally makes group-theoretic features
available via `passagemath-gap <https://pypi.org/project/passagemath-gap/>`_, `passagemath-groups <https://pypi.org/project/passagemath-groups/>`_, and `passagemath-nauty <https://pypi.org/project/passagemath-nauty/>`_::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-graphs[groups,test]" ipython
    In [1]: from passagemath_graphs import *

    In [2]: g = Graph({
                0: [1, 2],
                1: [0, 2],
                2: [0, 1, 3],
                3: [2]
            })

    In [3]: aut = g.automorphism_group()

    In [4]: print(aut.order())

``pip install passagemath-graphs[homology]`` provides homological computations for abstract complexes via `passagemath-modules <https://pypi.org/project/passagemath-modules/>`_.

``pip install passagemath-graphs[mip]`` additionally makes the mixed-integer programming
solver GLPK available via `passagemath-glpk <https://pypi.org/project/passagemath-glpk/>`_ and `passagemath-polyhedra <https://pypi.org/project/passagemath-polyhedra/>`_ (see there for other available solvers).::

    $ pipx run --pip-args="--prefer-binary" --spec "passagemath-graphs[mip,test]" ipython
    In [1]: from passagemath_graphs import *

    In [2]: ## Example depending on MIP goes here

``pip install passagemath-graphs[modules]`` additionally makes linear algebra features available via `passagemath-modules <https://pypi.org/project/passagemath-modules/>`_.

``pip install passagemath-graphs[plot]`` additionally installs `passagemath-plot <https://pypi.org/project/passagemath-plot/>`_.

``pip install passagemath-graphs[polyhedra]`` additionally installs `passagemath-polyhedra <https://pypi.org/project/passagemath-polyhedra/>`_.

``pip install passagemath-graphs[sat]`` additionally provides SAT features via `passagemath-combinat <https://pypi.org/project/passagemath-combinat/>`_.

``pip install passagemath-graphs[standard]`` installs all libraries and features related to graphs that
are available in a standard installation of Sage.


Development
-----------

::

    $ git clone --origin passagemath https://github.com/passagemath/passagemath.git
    $ cd passagemath
    passagemath $ ./bootstrap
    passagemath $ python3 -m venv graphs-venv
    passagemath $ source graphs-venv/bin/activate
    (graphs-venv) passagemath $ pip install -v -e pkgs/sagemath-graphs