We discuss the problem of ultrametricity in mean field spin glasses by means
of a hierarchical clustering algorithm. We complement the clustering approach
with quantitative testing: we discuss both in some detail. We show that the
elimination of the (in this context accidental) spin flip symmetry plays a
crucial role in the analysis, since the symmetry hides the real nature of the
data. We are able to use in the analysis disorder averaged quantities. We are
able to exhibit a number of features of the low T phase of the mean field
theory, and to claim that the full hierarchical structure can be observed
without ambiguities only on very large lattice volumes, not currently
accessible by numerical simulations.Comment: 15 pages with color figure
