Showing papers on "K-tree published in 1969"

A Note on the Detection of Cliques in Valued Graphs

Abstract: The theory of graphs has been used considerably in the study of social phenomena when it has been possible to conceive of such phenomena in terms of a set of units and of relations holding between these units. Such a conception of structure is readily handled by graph theory. Among the techniques that have been developed in this area is one of clique detection (Harary and Ross, 1957), where a clique is defined as a maximal subset of elements, each in reciprocal relation to the others. There are two principal drawbacks in using cliques as a concept of structure. Firstly, the definition of a clique places a severe restriction on what subsets are to be admitted as constituting a clique. Among a subset of elements that could form a clique, it only requires the absence of one reciprocal relation to disallow treating this subset of elements as a clique. A second drawback which is related to this, is that it is not possible to detect structural variation within a clique. While a clique is a set of units that are closely bound, it is not possible to examine whether or not some clique members are more closely bound together than others. It is possible to deal with the first of these problems by defining cliques in an alternative fashion that allows some of the reciprocal relations to be missing (Luce, 1950). Some of these alternative definitions are imprecise (Forsythe and Katz, 1946) and some lead to considerable difficulty in the detection of the modified clique. However, both of these problems may be viewed as stemming from the fact that there is insufficient information in the graph itself. If graphs are abstracted from, say, friendship choice, then to present this choice in all or