Measuring association in link-node problems

In this paper we have attempted to pose a methodological problem, and to provide answers to some fundamental measurement problems in research. In the search for the regularities which are thought to underlie the phenomena we study, geographers and others have often had recourse to Graph Theory to represent certain situations. Once some pattern of interaction can be depicted by using a group of points (nodes) joined by lines (links or edges), interest is often centered around the degree of correpondence between two graph-theoretic representations of empirical evidence. We have suggested methods for answering the question: are the link patterns for the two graphs so similar that they could not reasonably have arisen by chance? The approach to the solutions are based on probability theory and the properties of certain statistical distributions — the binomial, the hypergeometric, the hypergeometric?onominal and other combinations. In each case we have provided a rationale for the suggested solution as well as tables and computational procedures. The examples have been chosen from a wide variety of situations, for graph-theoretic representations are found in many fields of investigation.