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Khanra P, Ghosh S, Aleja D, Alfaro-Bittner K, Contreras-Aso G, Criado R, Romance M, Boccaletti S, Pal P, Hens C. Endowing networks with desired symmetries and modular behavior. Phys Rev E 2023; 108:054309. [PMID: 38115459 DOI: 10.1103/physreve.108.054309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Accepted: 10/18/2023] [Indexed: 12/21/2023]
Abstract
Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a synthetical structure being furthermore perfectly reflected in the modular organization of the network's functioning. Our results solve a relevant problem of designing a desired set of clusters and are of generic application in all cases where a desired parallel functioning needs to be blueprinted.
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Affiliation(s)
- P Khanra
- Department of Mathematics, State University of New York at Buffalo, Buffalo 14260, USA
| | - S Ghosh
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
| | - D Aleja
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
- Department of Internal Medicine, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - K Alfaro-Bittner
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - G Contreras-Aso
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - R Criado
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - M Romance
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - S Boccaletti
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
- CNR - Institute of Complex Systems, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141701, Russian Federation
- Complex Systems Lab, Department of Physics, Indian Institute of Technology, Indore - Simrol, Indore 453552, India
| | - P Pal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - C Hens
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
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Nazerian A, Panahi S, Leifer I, Phillips D, Makse HA, Sorrentino F. Matryoshka and disjoint cluster synchronization of networks. CHAOS (WOODBURY, N.Y.) 2022; 32:041101. [PMID: 35489844 PMCID: PMC8983070 DOI: 10.1063/5.0076412] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 03/14/2022] [Indexed: 06/14/2023]
Abstract
The main motivation for this paper is to characterize network synchronizability for the case of cluster synchronization (CS), in an analogous fashion to Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)] for the case of complete synchronization. We find this problem to be substantially more complex than the original one. We distinguish between the two cases of networks with intertwined clusters and no intertwined clusters and between the two cases that the master stability function is negative either in a bounded range or in an unbounded range of its argument. Our proposed definition of cluster synchronizability is based on the synchronizability of each individual cluster within a network. We then attempt to generalize this definition to the entire network. For CS, the synchronous solution for each cluster may be stable, independent of the stability of the other clusters, which results in possibly different ranges in which each cluster synchronizes (isolated CS). For each pair of clusters, we distinguish between three different cases: Matryoshka cluster synchronization (when the range of the stability of the synchronous solution for one cluster is included in that of the other cluster), partially disjoint cluster synchronization (when the ranges of stability of the synchronous solutions partially overlap), and complete disjoint cluster synchronization (when the ranges of stability of the synchronous solutions do not overlap).
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Affiliation(s)
- Amirhossein Nazerian
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Shirin Panahi
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Ian Leifer
- Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA
| | - David Phillips
- Department of Mathematics, United States Naval Academy, Annapolis, Maryland 21401, USA
| | - Hernán A. Makse
- Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA
| | - Francesco Sorrentino
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
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