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

Cobweb Posets and KoDAG Digraphs are Representing Natural Join of Relations, their diBigraphs and the Corresponding Adjacency Matrices