This paper considers derivable directed hypergraphs by undirected hypergraphs and generates undirected hypergraphs from directed hypergraphs. It tries to enumerate derivable directed hypergraphs and to find an upper bound for it. We introduce a positive relation on directed hypergraphs and derives digraphs via positive equivalence relation. We consider wireless sensor hypernetworks as directed hypergraphs and by clustering directed hypergraphs and positive equivalence relation obtain wireless sensor networks and show by cluster digraphs.
