  We summarize different approaches to the theory of quantum graphs and provide
several ways to construct concrete examples. First, we classify all undirected
quantum graphs on the quantum space $M_2$. Secondly, we apply the theory of
2-cocycle deformations to Cayley graphs of abelian groups. This defines a
twisting procedure that produces a quantum graph, which is quantum isomorphic
to the original one. For instance, we define the anticommutative hypercube
graphs. Thirdly, we construct an example of a quantum graph, which is not
quantum isomorphic to any classical graph.
