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

Jenna Birch, Athanasios A. Pantelous and Konstantin Zuev

Physica A: Statistical Mechanics and its Applications, 2015, vol. 417, issue C, 221-229

Abstract: 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.

Keywords: Planar Maximally Filtered Graphs; Correlation based Networks; 3- and 4-cliques; Eberhard’s operation; Standard spherical triangulation (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:417:y:2015:i:c:p:221-229

DOI: 10.1016/j.physa.2014.09.011

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