Tree representations of ternary relations

Abstract In recent years there has been a growing interest in representing data by trees. Most of the literature has been concerned with inferring trees from pairwise data. In this paper, trees are constructed from ternary relations; the model represents each object of an empirical set by a node of a tree so that a betweenness relation among the nodes (the node b is on the path from the node a to the node c) in the graph reflects a ternary relation among the objects. Various systems of formal properties that lead to three different kinds of tree representation are investigated.