I'm interested in two tasks:
- Find a decomposition (is it unique?) of a graph $G$ into its graphlets.
- Construct a graph starting from a set of graphlets.
What is the most efficient way to do it?
Unfortunately, I'm not very familiar with Spectral Graph Theory. I tried reasoning about the eigendecomposition of the Laplacian matrix, but it is not clear how a eigenvector correspond to a graphlet.
On the other hand, approaching the problem computationally has for me some issues, e.g. a 99 nodes graph has 33 3-graphlets or a node can belong to more than 1 graphlet?