Oriented Hypergraphs: Introduction and Balance

Abstract

An oriented hypergraph is an oriented incidence structure that extends the concept of a signed graph. We introduce hypergraphic structures and techniques central to the extension of the circuit classication of signed graphs to oriented hypergraphs. Oriented hypergraphs are further decomposed into three families—balanced, balanceable, and unbalanceable—and we obtain a complete classification of the balanced circuits of oriented hypergraphs.