Compatibility in a graph-theoretic setting (Q2367164)

A clustering is a type of classification imposed on the dissimilarities between objects. A cluster method can be interpreted as a mapping \(d\to F(d)\) of a measure \(d\) of dissimilarities of pairs of objects into a second measure \(F(d)\) that somehow summarises the information provided by \(d\). The input data to a monotone equivalent cluster method may be viewed as a nested sequence of undirected graphs, and a cluster method as a transformation of the given sequence into a second nested sequence of undirected graphs. The resulting approach is much easier to understand in the graph-theoretic setting. In this paper various types of cluster methods and their graph- theoretical interpretation are investigated.