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Metagraphs and Their Applications (Integrated Series in Information Systems)

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An important concept in the design of many information processing systems – such as transaction processing systems, decision support systems, and workflow systems – is that of a graph. In its simplest form a graph consists of a set of points (or nodes) and a set of ordered or unordered pairs of nodes (or edges). If the pairs of nodes are unordered, the graph is called a simple graph, and if they are ordered, the graph is called a directed graph, or digraph. In both cases, the graph represents a network through which materials, people, information, etc. can flow. The difference is whether the flow is restricted to one direction or whether there is no such restriction.

Simple graphs and digraphs allow for the construction of a variety of diagrammatic system design tools – such as entity-relationship diagrams, functional dependency diagrams, data flow diagrams, Petri nets, semantic nets, and the like. We note that most of these tools are representational, not analytical. That is, they provide a convenient and visually appealing format for illustrating information infrastructures, while allowing any subsequent analyses to be performed by the user.

Another problem with such graphical structures is that they usually associate individual information elements and not sets of elements. Yet in many cases it is necessary to associate sets of elements – such as multiple attributes in data relations, multiple variables in decision models, multiple logical variables in decision rules, and multiple documents in workflow systems. Furthermore, it may be necessary to integrate data relations, decision models, decision rules, and workflows into an integrated information processing system. Two multiple-element structures, hypergraphs and higraphs, allow a few such representations, but they have their limitations.
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