The Maximum Number of 3- and 4-Cliques within a Planar Maximally Filtered Graph
Mathematical Physics
2015-07-13 v1 Data Structures and Algorithms
math.MP
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
Cite
@article{arxiv.1507.02929,
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= {arXiv preprint arXiv:1507.02929},
year = {2015}
}
Comments
12 pages, 11 figures