I want to filter out networks/graphs which are just a single community rather than interconnected communities. Each community can either be a random graph or a star graph, but there should no community structure. The definition is loose considering that these data sets can have multiple communities with a varying number of edges connecting them together or nodes acting as bridging islands. (these networks are connected)
I thought of looking for networks where the average path length for at least 10% of the nodes is greater than 2.
I am using `MATLAB' and any reference to useful libraries would be appreciated.