Stars, maximal rectangles, lattices: a new perspective on Q-analysis

Abstract

A new star-hub structure of binary relations is discussed in the context of the methodology of Q-analysis, and parallels are drawn with maximal rectangles and Galois lattice structures. Although these structures generalize those of Q-analysis, there remain problems due to the very large number of star-hub pairs generated by fairly modest data sets. It is argued that more theory is necessary, and some possibilities are discussed. It is suggested that the criteria for defining new structures will come most fruitfully from the study of the relationship between backcloth and the ways it constrains traffic. Finally, it is argued that these combinatorial structures are still not sufficient to fully describe complex systems and that for this one needs to consider polyhedra in the context of N-ary relations.