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

Jenna Birch; Athanasios A. Pantelous; Konstantin Zuev

doi:10.1016/j.physa.2014.09.011

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 journal › Article › Research › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	221-229
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	417
DOIs	https://doi.org/10.1016/j.physa.2014.09.011
Publication status	Published - 1 Jan 2015
Externally published	Yes

Keywords

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

Access to Document

10.1016/j.physa.2014.09.011

Link to publication in Scopus

Cite this

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title = "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 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.",

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AU - Birch, Jenna

AU - Pantelous, Athanasios A.

AU - Zuev, Konstantin

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N2 - 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.

AB - 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.

KW - 3- and 4-cliques

KW - Correlation based Networks

KW - Eberhard's operation

KW - Planar Maximally Filtered Graphs

KW - Standard spherical triangulation

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JO - Physica A: Statistical Mechanics and its Applications

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