Spectral and Dynamical Invariants in a Complete Clustered Network

Authors

J. Leonel Rocha, Instituto Superior de Engenharia de Lisboa-ISEL, ADMand CEAUL, Rua Conselheiro Em´ıdio Navarro 1, 1959-007 Lisboa, PortugalFollow
Sara Fernandes, Mathematics Department, Universidade de ´Evora and CIMA-UE, Rua Rom?ao Ramalho 59, 7000-671 ´Evora, PortugalFollow
Clara Gr?cio, Mathematics Department, Universidade de ´Evora and CIMA-UE, Rua Rom?ao Ramalho 59, 7000-671 ´Evora, PortugalFollow
Acilina Caneco, Instituto Superior de Engenharia de Lisboa-ISEL, ADM and CIMA-UE, Rua Conselheiro Em´ıdio Navarro 1, 1959-007 Lisboa, PortugalFollow

Author Country (or Countries)

Portugal

Abstract

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.

Recommended Citation

Leonel Rocha, J.; Fernandes, Sara; Gr?cio, Clara; and Caneco, Acilina (2023) "Spectral and Dynamical Invariants in a Complete Clustered Network," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 19.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/19