Synchronization Reveals Topological Scales in Complex Networks
Physical Review LettersPublished 22 March 2006Open access
Àlex Arenas, Albert Dı́az-Guilera, Conrad J. Pérez-Vicente
Citations854
SJR quartileQ1
SJR score2.86
SNIP2.41
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators and provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.
Abstract
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.
Keywords
Computer ScienceBiochemistry, Genetics and Molecular BiologyPhysics and Astronomy
Reviews of Modern PhysicsStatistical mechanics of complex networks
20,607 Citations2002Réka Albert, Albert-Ĺaszló Barabási
A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.
Physical Review EFinding and evaluating community structure in networks
13,892 Citations2004Michelle G. Newman, Michelle Girvan
It is demonstrated that the algorithms proposed are highly effective at discovering community structure in both computer-generated and real-world network data, and can be used to shed light on the sometimes dauntingly complex structure of networked systems.
Physics ReportsComplex networks: Structure and dynamics
11,022 Citations2006Stefano Boccaletti, Vito Latora +3 more
The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
NatureExploring complex networks
8,339 Citations2001Steven H. Strogatz
This work aims to understand how an enormous network of interacting dynamical systems — be they neurons, power stations or lasers — will behave collectively, given their individual dynamics and coupling architecture.
Springer series in synergeticsChemical Oscillations, Waves, and Turbulence
7,124 Citations1984Yoshiki Kuramoto
The Geometry of Biological Time
3,584 Citations1980Arthur T. Winfree
Reviews of Modern PhysicsThe Kuramoto model: A simple paradigm for synchronization phenomena
3,501 Citations2005Juan A. Acebrón, L. L. Bonilla +3 more
In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model, and many variations and extensions of the original model that have appeared in the last few years are presented.
Journal of Statistical Mechanics Theory and ExperimentComparing community structure identification
2,877 Citations2005León Danon, Albert Dı́az-Guilera +2 more
It is found that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes.
Physical Review LettersMaster Stability Functions for Synchronized Coupled Systems
2,619 Citations1998Louis M. Pecora, Thomas L. Carroll
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsHierarchical organization in complex networks
2,183 Citations2003Erzsébet Ravasz Regan, Albert-Ĺaszló Barabási
The European Physical Journal BDetecting community structure in networks
2,022 Citations2004M. E. J. Newman
A number of more recent algorithms that appear to work well with real-world network data, including algorithms based on edge betweenness scores, on counts of short loops in networks and on voltage differences in resistor networks are described.
Physical Review LettersSynchronization in Small-World Systems
1,603 Citations2002Mauricio Barahona, Louis M. Pecora
Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes.
Sync: The Emerging Science of Spontaneous Order
1,240 Citations2003Steven H. Strogatz
Physical Review LettersHeterogeneity in Oscillator Networks: Are Smaller Worlds Easier to Synchronize?
846 Citations2003Takashi Nishikawa, Adilson E. Motter +2 more
It is found that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network distance is larger.
Physical Review ENetwork synchronization, diffusion, and the paradox of heterogeneity
547 Citations2005Adilson E. Motter, Changsong Zhou +1 more
This analysis reveals a striking relation between this process and the condition for the linear stability of the synchronized states and shows that, for a given degree distribution, the maximum synchronizability is achieved when the network of coupling is weighted and directed and the overall cost involved in the couplings is minimum.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsSpectra of “real-world” graphs: Beyond the semicircle law
481 Citations2001Illés J. Farkas, Imre Derényi +2 more
Methods to determine the eigenvalues of networks comparable in size to real systems are developed, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs.
Physical Review LettersSynchronization is Enhanced in Weighted Complex Networks
461 Citations2005Mario Chávez, Dong‐Uk Hwang +3 more
Journal of Statistical Mechanics Theory and ExperimentDetecting network communities: a new systematic and efficient algorithm
364 Citations2004Luca Donetti, Miguel A Muñoz
Physical Review LettersEntangled Networks, Synchronization, and Optimal Network Topology
343 Citations2005Luca Donetti, Pablo I. Hurtado +1 more
A new family of graphs, entangled networks, with optimal properties in many respects, is introduced, such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc.
Physica A Statistical Mechanics and its ApplicationsDetecting communities in large networks
331 Citations2005Andrea Capocci, Vito D. P. Servedio +2 more
An algorithm to detect community structure in complex networks based on spectral methods and takes into account weights and link orientation is developed, which proves to be successful both in clustering words, and in uncovering mental association patterns.
Europhysics Letters (EPL)Synchronization of Kuramoto oscillators in scale-free networks
283 Citations2004Yamir Moreno, A. F. Pacheco
It is found that the resynchronization time of a perturbed node decays as a power law of its connectivity, providing a simple analytical explanation to this interesting behavior.
Physical Review EFactors that predict better synchronizability on complex networks
241 Citations2004Hyunsuk Hong, Beom Jun Kim +2 more
The betweenness centrality is proposed as a good indicator for synchronizability and investigated the effects of various factors such as the degree, characteristic path length, heterogeneity, and betweennesscentrality on synchronization to find a consistent trend between the synchronization and the betweennessCentrality.
Physical Review EModular synchronization in complex networks
133 Citations2005Eunsoon Oh, Kyoohyoung Rho +2 more
It is found that the ST depends on the type of intermodular connections, and the exponent associated with the order parameter of the ST is found to be beta approximately 1 different from beta(MF) approximately 1/2 obtained from the scale-free network with the same degree distribution but the absence of modular structure.
Physical Review ESynchronization transition in scale-free networks: Clusters of synchrony
133 Citations2005Deok‐Sun Lee
The critical coupling strength and the order-parameter critical exponent derived by the mean-field approach depend on the degree exponent lambda, which implies a close connection between structural organization and the emergence of dynamical order in complex systems.
Physica A Statistical Mechanics and its ApplicationsFitness for synchronization of network motifs
74 Citations2004Yamir Moreno, M. Vázquez-Prada +1 more
The fitness for synchronization correlates well with motif's interconnectedness and structural complexity, and possible implications for present debates about network evolution in biological and other systems are discussed.