English

Extended Lorenz majorization and frequencies of distances in an undirected network

General Mathematics 2023-12-20 v1

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.

Keywords

Cite

@article{arxiv.2312.11472,
  title  = {Extended Lorenz majorization and frequencies of distances in an undirected network},
  author = {Leo Egghe},
  journal= {arXiv preprint arXiv:2312.11472},
  year   = {2023}
}