ACE

An Algebraic Combinatorics Environment for MAPLE providing functions to work with classical structures in algebraic combinatorics. Free download.

http://phalanstere.univ-mlv.fr/~ace/ACE/3.0/ACE.html

Algorithms and Software for Partitioning Meshes

Using combinatorics to solve structured linear systems of equations.

http://www.cs.sandia.gov/CRF/chac.html

Combinatorics Software of the Algorithms Project

Combinatorial analysis, discrete mathematics and computer algebra are the main interests of the Algorithms Projects. The packages let you define combinatorial structures; manipulate the associated generating functions, functional equations or recurrences; study their asymptotic behaviour.

http://algo.inria.fr/libraries/software.html

GRAPE

A GAP package for computing with graphs; primarily designed for the efficient construction and analysis of graphs related to groups, combinatorial designs and finite geometries.

http://www.maths.qmul.ac.uk/~leonard/grape/

Gato: The Graph Animation Toolbox

Software for visualizing graph algorithms. Free under GPL. Unix, Linux, MacOs and Windows versions.

http://gato.sourceforge.net/

GeoSteiner

Software for computing Steiner trees. Written in ANSI C, includes the public domain LP-solver lp_solve.

http://www.diku.dk/hjemmesider/ansatte/martinz/geosteiner/

Graph Coloring By DSATUR

By using the DSATUR algorithm, this php/form colors any graph in the Dimacs format.

http://prolland.free.fr/works/research/dsatphp/dsat.html

Graph Magics

A tool for graph theory, having a generator and offering various algorithms: shortest paths, network flows, maximal clique, optimal coloring etc.

http://www.graph-magics.com/

Graph Partitioners

Three algorithms written in NESL for finding separators of graphs, in order to compare the quality of the cuts.

http://www.cs.cmu.edu/~scandal/alg/separator.html

GraphThing

Tool for investigating Graph Theory, with a GTK interface. Free under GPL. Unix, source code in C++.

http://graph.seul.org/

Information-Theoretic GraphIsomorphism Algorithm

Provides a fast graphisomorphism algorithm written in object-oriented Java using the popular yfiles graph library. The ITGI algorithm can be freely downloaded.

http://www.itgi-algorithm.de/

LINK: A Software System for Discrete Mathematics

A general-purpose, extendible computing environment in which discrete mathematical objects representing real world problems can be easily manipulated and visualized.

http://dimacs.rutgers.edu/~berryj/LINK.html

METIS: Family of Multilevel Partitioning Algorithms

Graph, mesh, and hypergraph partitioning software.

http://glaros.dtc.umn.edu/gkhome/views/metis/

Nauty

A program for computing automorphism groups of graphs and digraphs. It can also produce a canonical labelling.

http://cs.anu.edu.au/~bdm/nauty/

NetworkX

NetworkX (NX) is a Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks.

http://networkx.github.io/

SCL - Star Complement Library

A program for computing the maximal graphs using the star complement technique including programs for computing the maximal cliques and the isomorphism classes of graphs.

http://www.math.rs/~zstanic/scl.htm

SF, Posets and Coxeter/Weyl

John Stembridge's Maple packages for symmetric functions, posets, root systems, and finite Coxeter groups.

http://www.math.lsa.umich.edu/~jrs/maple.html

graph-utils

A set of small utilities realizing theoretical graph algorithms (including tree algorithms). The utilities work with simple text input/output formats.

http://graph-utils.sourceforge.net/