Paths and cycles of hypergraphs

Hypergraphs are the most general structures in discrete mathematics. Acycli c hypergraphs have been proved very useful in relational databases. New sys tems of axioms for paths, connectivity and cycles of hypergraphs are constr ucted. The systems suit the structure properties of relational databases. T he concepts of pseudo cycles and essential cycles of hypergraphs are introd uced. They are relative to each other. Whether a family of cycles of a hype rgraph is dependent or independent is defined. An enumeration formula for t he maximum number of independent essential cycles of a hypergraph is given.