The degree of ultrametricity of a metric space

The notion of the degree of ultrametricity of a metric space is introduced. The degree of ultrametricity of the Euclidean space is obtained. The results of a statistical experiment on the computation of the degree of ultrametricity in the space of strings of given lengths for Hamming and edit distances are presented. It is shown that the degree of ultrametricity grows with an increase in the string length.