A Study of Roots of a Certain Class of Counting Polynomials

Modjtaba Ghorbani (), Razie Alidehi-Ravandi, Matthias Dehmer and Frank Emmert-Streib
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Modjtaba Ghorbani: Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785-163, Iran
Razie Alidehi-Ravandi: Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785-163, Iran
Matthias Dehmer: Department of Computer Science, Swiss Distance University of Applied Sciences, 3900 Brig, Switzerland
Frank Emmert-Streib: Predictive Society and Data Analytic Lab, Faculty of Information Technology and Communication Sciences, Tampere University, 33100 Tampere, Finland

Mathematics, 2023, vol. 11, issue 13, 1-14

Abstract: In this article, we introduce a new counting polynomial, namely the orbit polynomial. It is well-known that this polynomial has a unique positive zero δ in the interval [0, 1]. The aim of this paper is to study the specific properties of this polynomial and then determine the location of this root for several classes of complex networks to compare with other graphical measures. Additionally, we compare the unique positive zero measure with several well-known centrality graph measures.

Keywords: orbit polynomial; complex networks; automorphism group; entropy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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