<abstract xmlns="http://www.w3.org/1999/xhtml">

<sec>
<h3>Purpose</h3>
<p>To contribute to the study of networks and graphs.</p>
</sec>
<sec>
<h3>Design/methodology/approach</h3>
<p>We apply standard mathematical thinking.</p>
</sec>
<sec>
<h3>Findings</h3>
<p>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.</p>
</sec>
<sec>
<h3>Research limitations</h3>
<p>We restricted our investigations to undirected, unweighted networks.</p>
</sec>
<sec>
<h3>Practical implications</h3>
<p>We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property.</p>
</sec>
<sec>
<h3>Originality/value</h3>
<p>To the best of our knowledge our research contains new network results, especially those related to frequencies of distances.</p>
</sec>
</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.

Extended Lorenz majorization and frequencies of distances in an undirected network

Journal of Data and Information Science

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...

Extended Lorenz majorization and frequencies of distances in an undirected network

Article Category: Research Papers

Published Online: Feb 06, 2024

Page range: 1 - 10

Received: Nov 25, 2023

Accepted: Dec 28, 2023

DOI: https://doi.org/10.2478/jdis-2024-0007

Keywords
majorization, Lorenz curves, networks, shortest path distance, graphs

© 2024 Leo Egghe, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Figure 2.

Figure 3.

Extended Lorenz majorization and frequencies of distances in an undirected network

Article Category: Research Papers

Published Online: Feb 06, 2024

Page range: 1 - 10

Received: Nov 25, 2023

Accepted: Dec 28, 2023

DOI: https://doi.org/10.2478/jdis-2024-0007

Keywordsmajorization, Lorenz curves, networks, shortest path distance, graphs

© 2024 Leo Egghe, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Figure 2.

Figure 3.

Keywords
majorization, Lorenz curves, networks, shortest path distance, graphs