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. (c) 2007 Elsevier B.V. All rights reserved.