I want to write a program that creates action-oriented node-edge graphics similar to this video . What good C # libraries will allow me to do this?
If you're just looking for a .NET charting library, try QuickGraph http://quickgraph.codeplex.com/ . This is a universal graph library with many implemented algorithms and simple for unit test.
Graph # uses QuickGraph to render the Node Graph: http://graphsharp.codeplex.com/ I found this quite useful.