References to learn more about graph laplacian. I have vaguely heard of this connection between random matrix theory and graphs (the spectral gap of their laplacians) on compact Riemann surfaces. 


Can someone give a pedagogic reference which helps learn this subject? 
Also is there something called "free probability theory" which is somehow equivalent to random matrix theory? 
Would you call the usual QFT of Hermitian matrices a random matrix theory?
Suggest these free available resources. Most textbooks on graph theory only glance at "free probability theory". 

Lectures on the Combinatorics of Free Probability (London Mathematical Society Lecture Note Series): 
http://www.amazon.com/Lectures-Combinatorics-Probability-Mathematical-Society/dp/0521858526

Speicher lectures: http://www.mast.queensu.ca/~speicher/papers/lectures-IHP.pdf