  Correlations in Bell and noncontextuality inequalities can be expressed as a
positive linear combination of probabilities of events. Exclusive events can be
represented as adjacent vertices of a graph, so correlations can be associated
to a subgraph. We show that the maximum value of the correlations for
classical, quantum, and more general theories is the independence number, the
Lov\'asz number, and the fractional packing number of this subgraph,
respectively. We also show that, for any graph, there is always a correlation
experiment such that the set of quantum probabilities is exactly the
Gr\"otschel-Lov\'asz-Schrijver theta body. This identifies these combinatorial
notions as fundamental physical objects and provides a method for singling out
experiments with quantum correlations on demand.
