In the article ([Lovasz](http://www.cs.elte.hu/~lovasz/problems.pdf), section 1.3) mentions graph algebra structures on the set of formal linear combinations (over a field?) of a collection of graphs. He also mentioned quantum graphs as an example. My questions ( a question and one reference request ) are:


1. What is the relationship between graph algebra and quantum graph?
2. Could you suggest reference for graph algebra structures with the notion as in the linked article?



Graph algebras a la Lovasz
Question 1. is, strictly speaking, ungrammatical, and vague in most interpretations. If by *graph algebra* you mean *algebraic graph theory*, 
then the question is hopelessly broad. If by question 1. you mean 
``What is the relationship between *graph algebras* (in the sense of Lovász) and *quantum graphs* (also in the sense of Lovász), 
then the question is extremely specific and easy to answer: a quantum 
graph (in the sense of Lovász) is an *element* of a graph algebra 
(in the sense of Lovász). A definition of both these notions 
is given in e.g. 


Hatami, H. and Norine, S.: Undecidability of linear inequalities in graph homomorphism densities. Journal of the American Mathematical Society, Vol. 24, No. 2 (2011), p.547--565


which would also be my answer to Question 2. 
This is a good article to start, 
rich in mathematical context 
(e.g. Artin's solution of Hilbert's seventeenth problem).


