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Enhancing synchronizability of weighted dynamical networks using betweenness centrality.

Mahdi Jalili¹, Ali Ajdari Rad, Martin Hasler

¹Laboratory of Nonlinear Systems, School of Computer and Communication Sciences, Ecole Polytechnique Fédérale de Lausanne, CH 1015, Lausanne, Switzerland. Mahdi.Jalili@epfl.ch

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 4, 2008

Summary

This study introduces a novel network weighting method to improve synchronizability, a key property for dynamic systems. The technique enhances both general and phase synchronizability in various network types.

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Area of Science:

Complex Networks
Network Science
Dynamical Systems

Background:

Network synchronizability is crucial for the functioning of many complex systems.
Existing methods for enhancing synchronizability are limited.
The eigenratio of the graph Laplacian is a relevant measure for network synchronizability.

Purpose of the Study:

To propose and validate a novel network weighting procedure to enhance network synchronizability.
To investigate the effectiveness of the proposed method on different network topologies.
To explore the applicability of the method for enhancing phase synchronizability in networks of non-identical oscillators.

Main Methods:

Utilizing the eigenratio of the Laplacian as a synchronizability measure.
Employing node and edge betweenness centrality for network weighting.
Testing the method on scale-free, Watts-Strogatz, and random networks, as well as real-world graphs.

Main Results:

The proposed weighting procedure effectively enhances the synchronizability of various network types.
The method demonstrates robustness across different artificial and real-world network structures.
Numerical simulations confirm the enhancement of phase synchronizability for non-identical oscillators.

Conclusions:

The developed network weighting strategy is a powerful tool for improving the synchronizability of dynamical networks.
The method offers a practical approach for optimizing network performance in diverse applications.
The findings extend to improving the synchronization of coupled non-identical oscillators.