Hypernetworks in a directed hypergraph

Recently novel distributed approaches to the formation of collaborative networked organizations have been proposed. Some of them make use of logical–formal structures (i.e., hypernetworks and hyperpaths) based on concepts related to directed hypergraphs in order to formally represent competitive inter-cluster and collaborative intra-cluster relationships. In this paper, we introduce the concepts of • the s-hypernetwork, the structure consisting of all hyperpaths from a node s to any node in a directed hypergraph; • the (s,d)-hypernetwork, the structure consisting of all hyperpaths from a node s to a node d in a directed hypergraph. Moreover, we present characterization theorems for both structures, a polynomial algorithm to determine the s-hypernetwork and some conditions under which the problem of finding the (s,d)-hypernetwork is solvable in polynomial time.