  In this paper, we give a generalization of results in \cite{PU07} and
\cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie
superalgebras. In this way, we obtain a numerical invariant of quadratic Lie
superalgebras and a classification of singular quadratic Lie superalgebras,
i.e. those with a nonzero invariant. Finally, we study a class of quadratic Lie
superalgebras obtained by the method of generalized double extensions.
