Peripherality in networks: theory and applications

Jesse Geneson, Shen Fu Tsai

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish
Pages (from-to)1021-1079
Number of pages59
JournalJournal of Mathematical Chemistry
Issue number6
StatePublished - Jun 2022


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


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