1. Connectedness in a General Model for Valued Networks.
- Author
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Peay, Edmund R.
- Subjects
SOCIAL networks ,MATHEMATICAL models ,SIMULATION methods & models ,MATHEMATICAL functions ,SOCIAL groups ,INTERPERSONAL relations - Abstract
Social networks have been closely identified with graph theoretical models, which constitute their most familiar mode of representation. There are a number of such models which may embody symmetric, directed, or valued relationships. But the study of networks with valued linkages, using the natural formalization provided by the valued graph or digraph, has been impeded by a traditional lack of analytical machinery for dealing with valued structures. In this paper, we demonstrate the development and elaboration of formalizations for the central network concepts of reachability, joining, and connectedness through graph theoretical models of increasing complexity, culminating in their expression within a general model for valued structures. This model for valued (symmetric or directed) graphs, or vigraphs, provides a unified representation and matrix methodology for dealing with qualitative and quantitative structures, incorporates many existing methods as special cases, and suggests new applications. Some of the most interesting of these follow the recognition, consistent with the model, that the "values" assigned to network linkages may be sorts of entities other than numbers. [ABSTRACT FROM AUTHOR]
- Published
- 1980
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