We have $n$ nodes and an $n \times n$ probabilistic adjacency matrix $A$ such that $A_{ij}$ is the probability that an edge exists between nodes $i$ and $j$.
Our objective is to find the maximum probability graph of the nodes consisting entirely of disjoint cliques.
I assume that this is very hard to do optimally, however I'm curious about the kinds of approaches that are used to find good solutions to such problems. It seems deeply related, perhaps equivalent, to clustering.