  In this paper, we introduce a corresponding between bipartite graphs with a
perfect matching and digraphs, which implicates an equivalent relation between
the extendibility of bipartite graphs and the strongly connectivity of
digraphs. Such an equivalent relation explains the similar results on
$k$-extendable bipartite graphs and $k$-strong digraphs. We also study the
relation among $k$-extendable bipartite graphs, $k$-strong digraphs and
combinatorial matrices. For bipartite graphs that are not 1-extendable and
digraphs that are not strong, we prove that the elementary components and
strong components are counterparts.
