How to approach graphed data for a binary classification system? I'm looking for articles and other reading material on handling and modeling graph-shaped data for classification systems. As I've never working with graphed base machine learning anything from novice to advanced would be good. I'm after solving graph problems, but representing data that natively fits into a graph diagram in a way that would benefit machine learning on it.

I would like to experiment with predicting based on a graph of directed interactions between nodes in a system as well as incidental events occurring on one or more of the nodes (In hopes of deriving information from correlations between # of nodes similar incidents happened at, relations between nodes with similar incidents, etc).

Anything from published articles to experience tips and best practices would be highly appreciated.
Super comprehensive question. You are basically asking for tones of directions! I'd suggest to start with link prediction problem. So assume you have a directed/signed/weighted graph and you want to find the most probable next interaction (link/edge). I'd suggest to have a look at Jerome Kunegis papers and you may see it as a starting point and go on from there.