Minimum spanning trees (MST) and single linkage cluster analysis (SLCA) are explained and it is shown that all the information required for the SLCA of a set of points is contained in their MST. Known algorithms for finding the MST are discussed. They are efficient even when there are very many points; this makes a SLCA practicable when other methods of cluster analysis are not. The relevant computing procedures are published in the Algorithm section of the same issue of Applied Statistics. The use of the MST in the interpretation of vector diagrams arising in multivariate analysis is illustrated by an example.