I have an undirected graph representation of my system (a dynamical system), i.e. I have some labelled nodes and bi-directional edge weights, so everything is in a Markov matrix form.
Now I can form two copies of this Markov matrix: one from "real" data and another from "estimated data". I perform spectral clustering aka graph partitioning on these two graphs.
Theoretical results in my field show that clusters formed here are robust in some sense to errors from noise during estimation. There are some parameters in estimation process which I would like to tune by comparing the clusters formed from two data sets. What kind of norms/metrics are available to do this kind of comparison on clusters from two data sets.
Note that the Nodes are the same in both data sets. The clustering depends on the edge weights, and hence clusters from the two data set will be different.