Graph Animations with Combinatorica 
Combinatorica
(www.combinatorica.com)
is system for research and teaching
in discrete mathematics, particularly combinatorics and graph theory.
Combinatorica makes it easy
to construct graphs and other combinatorial objects, determine
their properties, and display them in revealing ways.
To highlight the power and beauty of Combinatorica graphics, we have put together a collection of animations of several important graphtheoretic topics and algorithms. For each animation, we provide an animated GIF file as well as a Mathematica notebook providing the code which we used to construct the animation.
See our associated book:
Computational Discrete Mathematics: Combinatorics and Graph Theory with
Mathematica by
Sriram Pemmaraju and
Steven Skiena,
Cambridge University Press, 2003 for more information about Combinatorica.

Animations: Breadth First Search/Depth First Search Evolution of Connected Components Hamiltonian Cycle Eulerian Cycle Dijkstra's Algorithm Transitive Closure with Graph Powering Minimal Spanning Tree 