Does somebody have some interesting references on the
FindGraphCommunties[.., Method -> "Spectral"] functions and their algorithms as implemented by Mathematica 9.
What the exact implementation is in Mathematica, I don't know. You can't know unless you have access to the source code or part of the research team. Assuming, however, that they used the fairly standard technique of spectral modularity maximization I hope these references are useful:
Modularity and community structure in networks, Proceedings of the National Academy of Science of the United States, vol. 103 no. 23. The preprint is also available. A nice introduction to spectral modularity maximization can be found in Networks by M.Newman, chapter 11.
Community detection modularity suite is an open source project which contains C++ and R implementations of the concepts explained in the articles.
An Effcient Spectral Algorithm for Network Community Discovery and Its Applications to Biological and Social Networks elaborates on a more efficient approach.