Hello people, i am an undergraduate student on computer science (so i don't have a strong background in physics) and i am very interested in quantum mechanics and its affection the way we see information. I am studying for my "thesis" (well it's not exactly thesis when you talk about undergraduate level) which is about quantum information/computation and quantum algorithms for several graph problems. The thing is, i fell upon some lecture slide notes of Peter Kuchment about quantum graphs defining them as: "A quantum graph Γ is a metric graph equipped with a self-adjoint operator H." I must admit i find it very hard to understand his notes since it has some first encountered words like "Sobolev spaces". My question is: What are the differences of quantum graph over the graphs we all know defined by graph theory? For example, can you say a quantum graph is Hamiltonian or traverse it? Any help would be appreciated!