  We present a package of mathematical theorems, which allow to construct
multipartite entanglement criteria. Importantly, establishing bounds for
certain classes of entanglement does not take an optimization over continuous
sets of states. These bonds are found from the properties of commutativity
graphs of operators used in the criterion. We present two examples of criteria
constructed according to our method. One of them detects genuine 5-qubit
entanglement without ever referring to correlations between all five qubits.
