Uncertainty relations from graph theory

Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured quantified through uncertainty relations. Although studied since inception theory, problem determining possible expectation values a collection remains, in general, unsolved. By constructing close connection between observables graph we derive relations valid for any set dichotomic observables. These are, many cases, tight, related size maximum clique associated graph. As applications, our results can be straightforwardly used formulate entropic relations, separability criteria entanglement witnesses.