How can Machine Learning be used to find attributes/characteristics of graphs? I am aware ML is not necessary for many graph classification problems (as the graph theorists have many clever solutions), but I'm specifically interested in ML approaches to these types of questions. I imagine if you had enough training examples (1000s?) you could use a supervised approach for classification type of questions. I also assume an adjacency matrix would be a good data representation to use for ML approaches to undirected graph classification. Example problems are shown below.

1.) Given an undirected graph represented by an adjacency matrix, broadly speaking, how (if possible) could machine learning be used to find if said graph has a hamiltonian path?

2.) Given an undirected graph represented by an adjacency matrix, how can ML be used to determine if the graph is a tree?
ML is not likely to be a good approach for these kinds of problems.  It will probably perform far worse than a hand-designed algorithm.  Current ML is not magic; it is just a form of pattern-matching.