I'm trying to find a way to find network communities in a top-down way. Most of the algorithms available (e.g. in the igraph package) are working bottom up - that is they start by assuming all nodes are singleton communities, and then combine them to larger communities. I want to got the other way around, similar to how decision trees are built: start with the whole network, then find a split that improves some "measure of information", etc.
Does anyone know of such algorithm or such a measure? I can't find such in the literature, but maybe I am missing something.
Also, what bothers me with some measures of modularity is that if you think of the whole network as one module, then all edges are within module and no out-module edges exist, so this seems like a perfect partition into a modules. Is there a measure that overcome this limitation?
I think Newman's algorithm meets your requirements.
It works by computing "network modularity" and then splitting the network into two groups. After that it recursively applies the same principle to the newly formed groups until no further increase in modularity is possible.
It should also be implemented in
igraph. At least in the r version.