I have a directed, weighted graph $G = (E,V)$. For example, one might be $|E| = 74000, |G| = 725$.
I want to divide this graph into two parts/clusters/communities, taking the edge weights into account.
I researched several methods, but the problem is that either they automatically detect the number of parts (communities), e.g. the Louvain method, or they only work for undirected graphs, e.g. k-MST. I also considered computing a minimum cut, but my network does not have source and sink.
Which other methods are there?