  The paper consider an equivalence relation in the set of vertices of a
bipartite graph. Some numerical characteristics showing the cardinality of
equivalence classes are introduced. A combinatorial identity that is in
relationship to these characteristics of the set of all bipartite graphs of the
type $g=\langle R_g \cup C_g, E_g \rangle$ is formulated and proved, where
$V=R_g \cup C_g$ is the set of vertices, $E_g$ is the set of edges of the graph
$g$, $ |R_g |=m\ge 1$, $|C_g |= n\ge 1$, $|E_g |=k\ge 0$, $m,n$ and $k$ are
integers.
