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.