[thewarrior]

What are some interesting kinds of graphs one can build this way and use them ?

[specproc]

Anything you want to look at over time. A social network is a classic: how a person's connections evolve over time or respond to temporal covariates.

Loads of stuff can be expressed as a graph though. I'm interested in natural language corpora as graphs, but as others have mentioned, there's neural networks here too. That's whatever you fancy these days.