The Maximum Number of 3- and 4-Cliques within a Planar Maximally Filtered Graph

Abstract

Planar Maximally Filtered Graphs (PMFG) are an important tool for filtering the most relevant information from correlation based networks such as stockmarket networks. One of themain characteristics of a PMFG is the number of its 3and 4-cliques. Recently in a few high impact papers it was stated that, based on heuristic evidence, the maximum number of 3and 4-cliques that can exist in a PMFGwith n vertices is 3n−8 and n−4 respectively. In this paper, we prove that this is indeed the case. © 2014 Elsevier B.V. All rights reserved.

DOI: 10.1016/j.physa.2014.09.011

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Cite this paper

@article{Birch2014TheMN, title={The Maximum Number of 3- and 4-Cliques within a Planar Maximally Filtered Graph}, author={Jenna Birch and Athanasios A. Pantelous and Konstantin Zuev}, journal={CoRR}, year={2014}, volume={abs/1507.02929} }