passagemath-graphs 10.8.5

passagemath: Graphs, posets, hypergraphs, designs, abstract complexes, combinatorial polyhedra, abelian sandpiles, quivers

passagemath is open source mathematical software in Python, released under the GNU General Public Licence GPLv2+.

It is a fork of SageMath, 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,

• providing independently usable Python interfaces to upstream libraries,

• offering platform portability and integration testing services to upstream projects,

• inviting collaborations with upstream projects,

• building a professional, respectful, inclusive community,

• empowering Sage users to participate in the scientific Python ecosystem by publishing packages,

• developing a port to WebAssembly (Pyodide, 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 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, with additional functionality from NetworkX and several other libraries.

What is included

• Graph Theory

• Trees

• Posets

• Abstract Complexes

• Combinatorial Designs and Incidence Structure

• Finite State Machines, Automata, Transducers

• Cluster Algebras and Quivers

• Knot Theory

• Sandpiles

• 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, passagemath-buckygen, and passagemath-plantri.

pip install passagemath-graphs[bliss] additionally installs passagemath-bliss for the purpose of computing graph (iso/auto)morphisms.

pip install passagemath-graphs[cliquer] additionally installs passagemath-cliquer

pip install passagemath-graphs[cmr] additionally installs 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 for group-theoretic functionality.

pip install passagemath-graphs[igraph] additionally installs igraph:

$ 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

pip install passagemath-graphs[nauty] additionally installs passagemath-nauty for computing automorphism groups of graphs and digraphs.

pip install passagemath-graphs[networkx] additionally installs NetworkX:

$ 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

pip install passagemath-graphs[planarity] additionally installs passagemath-planarity for planarity testing.

pip install passagemath-graphs[rankwidth] additionally installs passagemath-rankwidth for rank width and rank decompositions.

pip install passagemath-graphs[tdlib] additionally installs passagemath-tdlib for computing tree decompositions.

Features

pip install passagemath-graphs[combinat] additionally installs passagemath-combinat

pip install passagemath-graphs[editor] additionally installs the interactive graph editor phitigra.

pip install passagemath-graphs[groups] additionally makes group-theoretic features available via passagemath-gap, passagemath-groups, and 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.

pip install passagemath-graphs[mip] additionally makes the mixed-integer programming solver GLPK available via passagemath-glpk and 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.

pip install passagemath-graphs[plot] additionally installs passagemath-plot.

pip install passagemath-graphs[polyhedra] additionally installs passagemath-polyhedra.

pip install passagemath-graphs[sat] additionally provides SAT features via 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