  Since its popularization in the 1970s the Fiedler vector of a graph has
become a standard tool for clustering of the vertices of the graph. Recently,
Mendel and Noar, Dumitriu and Radcliffe, and Radcliffe and Williamson have
introduced geometric generalizations of the Fiedler vector. Motivated by
questions stemming from their work we provide structural characterizations for
when a finite metric space can be isometrically embedded in a Hilbert space.
