I'm trying to classify a certain family of Boolean functions, and need to represent the function as a graph. Is there any well-known graph representation for a Boolean function that captures the information that it is Boolean?
I'm presently using the variables as vertices with an edge between two if they are present in the same monomial. This does not take into account that the function is Boolean. I thought of 2-colorings of the vertices of a hypercube, but that does not really put any restriction on the graph. For my problem, I would need to use some property of the graph that results from the function being Boolean. Can someone provide some ideas to do this?