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An important concept in the design of many information processing systems — such as transaction processing systems, decision support systems, project management systems, and work flow systems — is that of a graph. In its simplest form, a graph consists of a set of elements (or nodes)and a set of ordered or unordered pairs of nodes (or edges). A substantial body of theoretical and applied research on various types of graphs has made it possible to develop powerful analytical tools for systems design. The purpose of this chapter is to summarize some of the existing graph-based tools used in this area, and the purpose of this book is to present a new graphical structure, called metagraphs, that enhances existing structures and overcomes some of their disadvantages.

In Chapter 1, the notion of a metagraph was introduced informally, using visual depictions and descriptions. In this chapter, the formal structure of a metagraph is defined, and its basic properties are identified.

In this chapter, we further develop the connectivity features of paths and metapaths introduced in Chapter 2. In particular, we introduce the notions of bridges, cycles and the properties of dominance.

So far, we have considered a variety of features of a metagraph, where these features are specified in terms of the metagraph structure as given. However, there are many situations where it may be desirable to transform the given structure of a metagraph into another form that more effectively discloses certain structural features and/or facilitates certain analyses. In this chapter, we explore the transformation of a metagraph from one form to another that provides a different view of the system and/or relationships described by the metagraph.

As described thus far, metagraph edges are set-to-set mappings with no further information attached. However, it is possible to attach attributes to metagraph edges. In this chapter, we examine how both qualitative and quantitative attributes can be added to metagraph edges.

We now examine the issue of independence of a sub-metagraph contained within a larger metagraph. This is a useful notion, since it helps identify components of a larger and complex system that can be abstracted a a higher level, and possibly removed as a separate subsystem.

This is the first of three chapters in which we will examine three applications of metagraphs to information processing systems. The first is the application to the management of decision models, which is examined in this chapter. The second is the management of data bases and rule bases, which will be examined in Chapter 8. The third is the management of workflow systems, in which the work consists of information processing tasks to be performed by humans or machines. We will examine this application in Chapter 9.

We now extend the results of Chapter 7 to encompass two additional information structures. The first is data bases, in which each edge represents a data relation with the key attributes as invertex and content attributes as outvertex. The second information structure is rule bases in which each edge represents a production rule with the antecedent (as a conjunction of propositions) as invertex and the consequent (also as a conjunction of propositions) as outvertex.

This is the last of the three chapters in which we examine the applications of metagraphs to information processing systems. In the previous two chapters we examined applications to three information structures found in decision support systems: data, models, and rules. We now turn to yet another topic — workflow systems. Workflow systems integrate the judgmental and decision making efforts of humans (managers and analysts)with the information processing (computational and communication)activities of machines to implement business processes.

We have now completed our presentation of metagraph theory and applications. We began by defining a metagraph as a collection of directed set-to-set mappings, where the sets are subsets of a generating set, at most one of the sets in any edge is null, and for any edge the two sets defining the edge are disjoint. We then developed an algebraic theory of metagraphs and applied it to metagraph connectivity, metagraph transformations (especially projection), assignment of attributes to edges, assumptions and conditional metagraphs, and the properties of sub-metagraphs. Finally we examined the application of metagraphs to the structuring of decision support (i.e., data, model, and rule management) systems and workflow systems.