Peripherality in networks: theory and applications

Publication Date

6-1-2022

Document Type

Article

Publication Title

Journal of Mathematical Chemistry

Volume

60

Issue

6

DOI

10.1007/s10910-022-01345-8

First Page

1021

Last Page

1079

Abstract

We investigate several related measures of peripherality and centrality for vertices and edges in networks, including the Mostar index which was recently introduced as a measure of peripherality for both edges and networks. We refute a conjecture on the maximum possible Mostar index of bipartite graphs. We asymptotically answer another problem on the maximum difference between the Mostar index and the irregularity of trees. We also prove a number of extremal bounds and computational complexity results about the Mostar index, irregularity, and measures of peripherality and centrality. We discuss graphs where the Mostar index is not an accurate measure of peripherality. We construct a general family of graphs with the property that the Mostar index is strictly greater for edges that are closer to the center. We also investigate centrality and peripherality in two graphs which represent the SuperFast and MOZART-4 systems of atmospheric chemical reactions by computing various measures of peripherality and centrality for the vertices and edges in these graphs. For both of these graphs, we find that the Mostar index is closer to a measure of centrality than peripherality of the edges. We also introduce some new indices which perform well as measures of peripherality on the SuperFast and MOZART-4 graphs.

Funding Sponsor

National Aeronautics and Space Administration

Keywords

Centrality, Mostar Index, MOZART-4, Peripherality, Sum peripherality, SuperFast, Terminal Mostar Index, Total Mostar Index

Department

Mathematics and Statistics

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