  Natural join of $di-bigraphs$ that is directed biparted graphs and their
corresponding adjacency matrices is defined and then applied to investigate the
so called cobweb posets and their $Hasse$ digraphs called $KoDAGs$. $KoDAGs$
are special orderable directed acyclic graphs which are cover relation digraphs
of cobweb posets introduced by the author few years ago. $KoDAGs$ appear to be
distinguished family of $Ferrers$ digraphs which are natural join of a
corresponding ordering chain of one direction directed cliques called
$di-bicliques$. These digraphs serve to represent faithfully corresponding
relations of arbitrary arity so that all relations of arbitrary arity are their
subrelations. Being this $chain -way$ complete if compared with kompletne
$Kuratowski$ bipartite graphs their $DAG$ denotation is accompanied with the
letter $K$ in front of descriptive abbreviation $oDAG$. The way to join
bipartite digraphs of binary into $multi-ary$ relations is the natural join
operation either on relations or their digraph representatives. This natural
join operation is denoted here by $\os$ symbol deliberately referring to the
direct sum $\oplus$ of adjacency matrices as it becomes the case for disjoint
$di-bigraphs$.
