Ordinal network representation: Representing proximities by graphs (Q2277198)

The author considers ordinal network representations as graph-theoretical representations of proximity data by means of the minimum-path-length distance of a connected and weighted graph. In contrast to traditional tree-based graph-theoretic approaches, the ordinal network representation is not limited to but includes the representation by trees. The paper explores fundamental representation and uniqueness results and discusses a method of constructing ordinal network representations. A simple strategy for handling the problem of errors in the data is described and illustrated.