  We develop a numerical algorithm to calculate the degrees of irreducible
multiparty correlations for an arbitrary multiparty quantum state, which is
efficient for any quantum state of up to five qubits. We demonstrate the power
of the algorithm by the explicit calculations of the degrees of irreducible
multiparty correlations in the 4-qubit GHZ state, the Smolin state, and the
5-qubit W state. This development takes a crucial step towards practical
applications of irreducible multiparty correlations in real quantum many-body
physics.
