[jmj42]

It's funny you should mention graph theory and network security. I'm involved in cyber security research, though more on the operations side of security than networks. However, our research group does do quite a bit of work on the network side. Most of it's focused on SCADA networks, but there's a couple of really cool tools (read startups) that have come out of our group that lean heavily on graph theory.

NP-View[1] maps connections. That is, If HostA can reach HostB, and HostB can reach HostC, is there a path from HostC to HostA.

Veriflow (which I know far less about) is a large topology mapping tool.

[1] http://www.network-perception.com/ [2] http://www.veriflowsystems.com/