On A Graph Formalism for Ordered Edges

Abstract

Though graphs are flexible enough to model any kind of data structure in principle, for some structures this results in a rather large overhead. This is for instance true for lists, i.e., edges that are meant to point to an ordered collection of nodes. Such structures are frequently encountered, for instance as ordered associations in UML diagrams. Several options exist to model lists using standard graphs, but all of them need auxiliary structure, and even so their manipulation in graph transformation rules is not trivial.

In this paper we propose to enrich graphs with special ordered edges, which more naturally represent the intended structure, and define how lists can be manipulated. We show that the resulting category satisfies sufficient HLR properties to apply standard algebraic graph transformation. We believe that in a context where lists are common, the cost of a more complicated graph formalism is outweighed by the benefit of a smaller, more appropriate model and more straightforward manipulation.