Software

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

Free Software in Graph Theory
Free Software for Win 9X,NT on Graph Theory by Vitali Petchenkine. Procedures: Metrics of the graph; Paths and cycles; Colorations; Automorphism group; Minimal spanning tree; Shortest paths; Max. Capacity path; K Shortest paths; Salesman problem; Maximal flow; Critical path; Reports for Graphs; Print.
http://www.geocities.com/pechv_ru/

Gato: The Graph Animation Toolbox
Software for visualizing graph algorithms. Free under GPL. Unix, Linux, MacOs ad Windows versions.
http://www.zpr.uni-koeln.de/~gato

GeoSteiner
Software for computing Steiner trees. Written in ANSI C, includes the public domain LP-solver lp_solve.
http://www.diku.dk/geosteiner/

GOBLIN Graph Library
C++ library of graph optimization algorithms with a GUI for editing, running and tracing the algorithms.
http://www.math.uni-augsburg.de/opt/goblin.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/

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/

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

Information System on Graph Class Inclusions
A java applet for researching what is known about particular graph classes.
http://wwwteo.informatik.uni-rostock.de/isgci/

JGraphT
Free Java class library that provides mathematical graph-theory objects and algorithms.
http://jgrapht.sourceforge.net

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://www-users.cs.umn.edu/~karypis/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/

plantri and fullgen
Programs for generation of certain types of planar graph, generated in such a way that exactly one member of each isomorphism class is output without the need for storing them.
http://cs.anu.edu.au/people/bdm/plantri/

SCL - star complement library
A program for calculating the maximal graphs using the star complement technique. The programs for computing the maximal cliques and isomorphism classes of graphs are included.
http://www.matf.bg.ac.yu/%7ezstanic/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