Which machine learning approach/algorithm do I choose for path validation? I apologize for lack of terminology, I'm no computer scientist.
I have a problem of validating paths in a directed graph with complex nodes.

The full description is the following:


I have a decent set (about 1K) of directed graphs;
Each node contains a complex data structure (it is a hierarchical data structure, not a picture or sound);
I have some of paths in those graphs known as "correct" paths (based
mostly on data in nodes);
And I have some of paths in those graphs known as "incorrect" paths
(with classification why it is incorrect).


I'd like to predict given a graph with those complex nodes and a path, is this path "correct".

Which machine learning algorithm will suit me best?
In general, what approach I should use?

Edit:


Each full graph is either have app paths processed
(correct/incorrect) or completely blank (no path is processed);
Correctness depends on both position of node in a graph AND data in
the node;
Humans would need heuristics to decide or guess which paths are
correct;
Most of the paths are "correct";
I hope to convert human heuristics to some kind of "correctness"
recognition.
This is a good question but it's rather complicated. I can suggest two approaches:


Graphical models; specifically Bayesian networks since your graph is directed.
Recurrent neural networks. Here's a talk on popular recent model: Sequence to Sequence Learning with Neural Networks.