Extended Lorenz majorization and frequencies of distances in an undirected network
| 06 lut 2024
O artykule
Article Category: Research Papers
Data publikacji: 06 lut 2024
Zakres stron: 1 - 10
Otrzymano: 25 lis 2023
Przyjęty: 28 gru 2023
DOI: https://doi.org/10.2478/jdis-2024-0007
Słowa kluczowe
© 2024 Leo Egghe, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
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.