  A linear operator on a Hilbert space $\mathbb{H}$, in the classical approach
of von Neumann, must be symmetric to guarantee self-adjointness. However, it
can be shown that the symmetry could be ommited by using a criterion for the
graph of the operator and the adjoint of the graph. Namely, S is shown to be
densely defined and closed if and only if $\{k + l : \{k, l\} \in G(S) \cap
G(S)^*\} = \mathbb{H}$. In a more general setup, we can consider relations
instead of operators and we prove that in this situation a similar result
holds. We give a necessary and sufficient condition for a linear relation to be
densely defined and self-adjoint.
