The maximum number of 3- and 4-cliques within a planar maximally filtered graph

Jenna Birch, Athanasios A. Pantelous, Konstantin Zuev

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)


Planar Maximally Filtered Graphs (PMFG) are an important tool for filtering the most relevant information from correlation based networks such as stock market networks. One of the main characteristics of a PMFG is the number of its 3- and 4-cliques. Recently in a few high impact papers it was stated that, based on heuristic evidence, the maximum number of 3- and 4-cliques that can exist in a PMFG with n vertices is 3n-8 and n-4 respectively. In this paper, we prove that this is indeed the case.

Original languageEnglish
Pages (from-to)221-229
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Publication statusPublished - 1 Jan 2015
Externally publishedYes


  • 3- and 4-cliques
  • Correlation based Networks
  • Eberhard's operation
  • Planar Maximally Filtered Graphs
  • Standard spherical triangulation

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