# How is this graphical representation of SAT/CSP instances called?

Given a CNF formula (SAT problem), we can construct the constraint/dependency graph, which contains a vertex for each variable and a hyperedge for each clause. Same goes for CSPs, where we have a hyperedge for each constraint.

But given a CNF formula, we could also define a (slightly larger) graph that has literals as vertices and clauses as hyperedges, where each edge is incident to each literal it contains. This can analogously be done for a CSP.

How is the latter graph called?

This has been called the microstructure complement when the edges represent the forbidden partial assignments. I personally prefer the term clause structure. The clause structure of a constraint satisfaction problem instance is obtained by applying the direct encoding of the instance to SAT, where each possible value $a$ of variable $v$ is represented by a literal $(v,a)$, the forbidden partial assignments are SAT clauses involving these literals, and a clause $\{(v,a),(v,b)\}$ is added for every variable $v$ and any values $a\ne b$. (These clauses force a solution to be a function, assigning at most one value to each variable.)