Abstract
The topological ultrametricity index can be approximated by the expected survival time of a dataset in the state of being ultrametric while only distances up to a given value are considered. It is observed that the quotient of the number of connected components by the number of maximal cliques in the Vietoris-Rips graph initially is the survival function of a Weibull distribution. This is shown for some codings of Fisher's Iris data as well as for random samples in the Euclidean hypercube.
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