Which unsupervised method can infer explicit interaction from occurance(count) data?

[wanglu2014]

Our input data is a table of edges (edge weight is implicit interaction, which weighted with co-occurrence, edge type was also implicit which inferred from prior knowledge) and a list of nodes (two types: users and items). Group-truth is a small set of edges that are known to exist. The ground-truth set is too small to train a model, therefore, we want to do unsupervised analysis. For example:

edgetable.csv (potential edges) dst | src | attr A | B | edgetype1 A | B | edgetype2 A | C | edgetype1 B | D | edgetype1

nodetable nodeID | type | sample1(count) | sample2(count) | sample3(count) A | nodetype2 | 5 | 6 | 8 B | nodetype1 | 3 | 5 | 9 C | nodetype1 | 2 | 4 | 6 D | nodetype2 | 5 | 2 | 5

ground-truth B D edgetype1

Our purpose is twofold:

Whether there is an explicit interaction between two types of nodes turely exist in given samples?
How to determine the edge type?

Thank you for your help！