links is obtained when q = n − 1 and r = ∞, i.e., PFnet(n − 1, ∞). With ordinal-scale data (see level of measurement), the r-parameter should be infinity because the same PFnet would result from any positive monotonic transformation of the proximity data. Other values of r require data measured on a ratio scale. The q parameter can be varied to yield the desired number of links in the network. Essentially, pathfinder networks preserve the shortest possible paths given the data so links are eliminated when they are not on shortest paths. The PFnet(n − 1, ∞) will be the minimum spanning tree for the links defined by the proximity data if a unique minimum spanning tree exists. In general, the PFnet(n − 1, ∞) includes all of the links in any minimum spanning tree. References Further information on pathfinder networks and several examples of the application of PFnets to a variety of problems can be found in: Schvaneveldt, R. W. (Ed.) (1990) Pathfinder Associative Networks: Studies in Knowledge Organization. Norwood, NJ: Ablex. The book is out of print. A zipped copy of pdf chapters can be downloaded: zip A shorter article summarizing pathfinder networks: Schvaneveldt, R. W., Durso, F. T., & Dearholt, D. W. (1989). Network structures in proximity data. In G. Bower (Ed.), The psychology of learning and motivation: Advances in research and theory, Vol. 24 (pp. 249–284). New York: Academic Press. pdf Three papers describing fast implementations of pathfinder networks: (The two variants by Quirin et al. are significantly faster. While the former can be applied with q = 2 or q = n − 1 and any value for r, the latter can only be applied in cases where q = n − 1 and r = ∞.) External links List of papers using Pathfinder Pathfinder Software Download Site Implementation of the original, Binary, Fast and MST variants of the algorithm in C Comparison table between the different variants Psychometrics