Although (in my totally unbiased opinion) Combinatorica is more comprehensive and better integrated than other libraries of combinatorial algorithms, it is also the slowest such system available. Credit for all of these properties is largely due to Mathematica, which provides a very high-level, functional, interpreted, and thus inefficient programming language. Combinatorica is best for finding quick solutions to small problems, and (if you can read Mathematica code) as a terse exposition of algorithms for translation into other languages.

Combinatorica is best described in my book:

Steven S. Skiena, Implementing Discrete Mathematics: Combinatorics and Graph Theory in Mathematica , Advanced Book Division, Addison-Wesley, Redwood City CA, June 1990. ISBN number 0-201-50943-1. Japanese translation published by Toppan, Tokyo, July 1992.

Combinatorica is included with the standard Mathematica distribution in the directory Packages/DiscreteMath/Combinatorica.m . It can also be obtained by anonymous ftp from ftp.cs.sunysb.edu in the directory pub/Combinatorica. For this FTP site with the latest version of Combinatorica, databases of interesting graphs, and related programs, click here