I was looking for a value of how clustered a network is. I thought that somewhere in graph spectrum was a good place to start and that in the Python package NetworkX there would be some useful methods. However, I couldn’t immediately see any good methods in NetworkX. Then Morten Mørup mentioned something about community detection and modularity and I became diverged, but now I am back again at the graph spectrum.
The second smallest eigenvalue of the Laplacian matrix of the graph seems to represent reasonably well what I was looking for. Apparently that eigenvalue is called the Algebraic connectivity.
NetworkX has a number of graph generators, and for small test cases the algebraic connectivity seems to give an ok value for how clustered the network is, – or rather how non-clustered it is.