Could someone suggest me a good introductory book or an article on graph clustering?
The book The Elements of Statistical Learning by Trevor Hastie,
Robert Tibshirani and
Jerome Friedman covers a lot of learning and clustering algorithms including various graph clustering algorithms. Algorithms such as Spectral Clustering are phrased algebraically, as is much of the book. The good thing is that a pdf of the book is available from the authors' website, linked above. It has an extensive bibliography to help you beyond what is presented in the book.

There's also an implementation of Spectral Clustering in R which works quite well and has lots of options.