  Distinct from Bell's approach, Wigner had derived a form of local realist
(LR) inequality which is quantum mechanically violated for a bipartite
maximally entangled state. Subsequently, this approach was generalized to
obtain a multipartite LR inequality. However, the violation of such generalised
Wigner's inequality does not guarantee nonlocality between all possible
different bipartitions of the multipartite system. In the present work, this
limitation has been overcome by formulating a further generalisation of
Wigner's approach through the derivation of a set of LR inequalities with
respect to all different bipartitions of a N-partite system. Quantum mechanical
violations of all individual LR inequalities belonging to such a set would
rigorously certify multipartite nonlocality by also providing a finer
characterisation of the nature of multipartite nonlocality in the following
sense. The quantum mechanical violation of any given inequality of our complete
set of LR inequalities would enable identification of the corresponding
bipartition which exhibits nonlocality. This is in contrast to other
multipartite LR inequalities such as the Svetlichny inequality or its
generalisation that cannot be used to detect whether there is any particular
bipartition which is nonlocally correlated. The efficacy of the scheme
developed in this paper is illustrated for the tripartite and quadripartite
states.
