  We introduce adequate concepts of expansion of a digraph to obtain a
sequential construction of minimal strong digraphs. We characterize the class
of minimal strong digraphs whose expansion preserves the property of
minimality. We prove that every minimal strong digraph of order $n\geq 2$ is
the expansion of a minimal strong digraph of order $n-1$ and we give
sequentially generative procedures for the constructive characterization of the
classes of minimal strong digraphs. Finally we describe algorithms to compute
unlabeled minimal strong digraphs and their isospectral classes.
