Describe a graph through logic

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At the moment I'm in need to learn how to describe a graph through a logic statement such as:

$$ \forall x\forall y(r(x,y) \to \lnot s(y,x) \land \lnot s(y,x)) \land \exists (s(z,z) \land \lnot r(z,z)$$

Where can I find a paper, document or any other useful source to learn how to draw a graph from such a formula and (eventually) viceversa?