| Abstract: | Networt unfolding is a measurement model for representing relational dta by a connected and weighted graph. If the data — partial or complete rank orders — can be represented by such a graph then the complete graph yields a representation. However, our aim is to minimize the number of lines in the representation and to find a maximally reduced graph. The maximally reduced graph for a specific set of a data may not be a tree but may contain one or more cycles. THe scale level of the weights is at least that of an ordered metric scale.Four examples are provided to illustrate the model and the algorithm to find the reduce graph. The first example serves to introduce the terms and notations and represents the similarity of Apachean languages. The communication network of the second example on the network structure of exchange of positive messages as a directed graph. In the third example on the network structure of human associative memory we show by means of Monte Carlo study that the obtained reduction of the graph is larger than to be expected by chance, and infer that the structure is different from that assumed by Anderson and Bower. In the fourth example on popularity status we conceive status as a social agreement structure.We consider network unfolding to be an alternative to other models of strucuture as, e.g. multidimensional scaling, cluster, and factor analysis. Substantial theory should guid the selection among these models. |
