Classifications by Multigraphs: Three Examples from Medicine

Abstract

Calculus of graph theory provides researchers of different topics with a model to simulate many systems — especially in applied mathematics and life sciences. Cluster analysis or numerical taxonomy is one example. Though usually, in taxonomy, clusters are nothing more than the result of an algorithm, graph theory makes it possible to define clusters properly in mathematical terms. One convenient definition — as shown in Subsections 3.1.2 and 3.2.2 — is to speak of (single-linkage) clusters as components of a graph Γ(d) or as s-components of a multigraph Γ $({\vec d^T})$ . Beyond the possibility to define clusters mathematically, graph theory provides the scientist with tools to formulate and test null hypotheses on the structures of data sets. Thus, cluster analysis is raised from a tool of exploratory statistics to a helpful method of inference statistics.