  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.
