You can use free Microsoft Chart Controls for both ASP.NET and WinForms.
Take a look at yWorks: http://www.yworks.com/en/index.html
There aren't a massive amount of good libraries out there, from what I've seen.
There is QuickGraph, it works pretty well and has most of the basic algorithms.
Check out http://quickgraph.codeplex.com/ They have support for visualization via DotViz and Glee.
For visualization, i'd also check out
Though its flash, it seems very interesting, and they have at least tree visualization, though you may be able to coax some non-directed graphs out of it.
You can use the NodeXL API from Microsoft Research at: http://www.codeplex.com/NodeXL but a similar question has been asked at: http://stackoverflow.com/questions/44090/do-you-know-any-graph-visualization-libraries-for-net/
Buddy I think this is what you need!
This article presents a Generic Graph Library, 100% C#. This library is an attempt to port the Boost Graph Library (BGL) from C++ to C#.
I haven't tried it yet but ran across an interesting offering from MS Research for visualizing directed graphs Microsoft Automatic Graph Layout.
Try using "directed graph" or "digraph" for search terms. I get a lot of hits.
Use a combination of QuickGraph and Graph# (WPF) - both top notch libraries. They work really well for me but the documentation for Graph# is almost non-existant.