Converting high-dimensional complex networks to lower-dimensional ones preserving synchronization features

¹ Department of Biomedical Engineering, Amirkabir University of Technology (Tehran polytechnic) - Tehran, Iran
² Health Technology Research Institute, Amirkabir University of Technology (Tehran polytechnic) - Tehran, Iran
³ Institut für Theoretische Physik, Technische Universität Berlin - Hardenbergstrasse 36, 10623 Berlin, Germany
⁴ Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität - 10115 Berlin, Germany
⁵ Potsdam Institute for Climate Impact Research - Telegrafenberg A 31, 14473 Potsdam, Germany
⁶ Humboldt University Berlin, Department of Physics - Berlin, 12489, Germany

^(a) E-mail: sajadjafari@aut.ac.ir (corresponding author)

Received: 4 August 2022
Accepted: 10 October 2022

Abstract

Studying the stability of synchronization of coupled oscillators is one of the prominent topics in network science. However, in most cases, the computational cost of complex network analysis is challenging because they consist of a large number of nodes. This study includes overcoming this obstacle by presenting a method for reducing the dimension of a large-scale network, while keeping the complete region of stable synchronization unchanged. To this aim, the first and last non-zero eigenvalues of the Laplacian matrix of a large network are preserved using the eigen-decomposition method and Gram-Schmidt orthogonalization. The method is only applicable to undirected networks and the result is a weighted undirected network with smaller size. The reduction method is studied in a large-scale a small-world network of Sprott-B oscillators. The results show that the trend of the synchronization error is well maintained after node reduction for different coupling schemes.