Extended Lorenz majorization and frequencies of distances in an undirected network

Abstract

Findings: We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain. As a consequence, the average and median distances in any such network are smaller than or equal to those of a chain. Research limitations: We restricted our investigations to undirected, unweighted networks. Practical implications: We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property.