Extended Lorenz majorization and frequencies of distances in an undirected network

Abstract

Purpose To contribute to the study of networks and graphs. Design/methodology/approach We apply standard mathematical thinking. 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. Originality/value To the best of our knowledge our research contains new network results, especially those related to frequencies of distances.