A graph theoretic model of data structures

The widespread development of large shared data bases has proceeded mainly on empirical notions. Only in the past few years have there been attempts at formalizing the underlying concepts into a theory of data structures. The present models have been founded on the well-established mathematical theories of sets, relations and graphs, but few descriptions have been sufficiently developed to meet the needs of a complete theory of data structures. The set theoretic formalism offered by Childs(1) or Schwartz(2) or the relational model by Codd(3) are useful but fail to give a complete description of the complex structures found in modern data bases. The graph theoretic concepts found in papers by Harary and Hsiao(4) and Earley(5) are more appealing but need further elaboration. This paper is an attempt to develop a graph theoretic model into a useful formalism for describing and manipulating data structures.