Spectral Algorithms and Spectral Graph Theory
There are a number of great monographs and lecture notes for Spectral Graph Theory. My favourites are:
I am teaching a Spectral Graph Theory class at BU. Here is the Fall 2016 version.
A classical source for Spectral Graph Theory is Fan Chung’s book.
Connection to Semidefinite Programming
My preffered way to think about spectral algorithms is through the lens of SDP optimization. See these papers of mine for examples: