Synchronization reveals topological scales in complex networks.

By Alex Arenas, Albert Díaz-Guilera, C. Pérez-Vicente. Physical Review Letters, 2005

785 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/36da5493b082c5692e794e0283eaf3260c451811

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Molecular Biology

In Statistical and Nonlinear Physics

Citations in the corpus

Analysis of the structure of complex networks at different resolution levels (2007, background): “Although, in principle, all resolution scales provide some information about the topology, and are important, the detection of partitions that are more persistent than the rest when changing the resolution r is indicative of a tougher modular structure.”
Community Structure in Graphs (2007, neutral): “This was ﬁrst shown by Arenas, D´ıaz-Guilera and P´erez-Vicente [77].”
Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks (2008, background): “…particularly relevant when the network is composed of tightly-knit modules or communities [4], [5], [6], [7], [8], [9], which can lead, for instance, to partially coherent dynamics [10], [11], or to the emergence of co-operation [12] and coexistence of heterogeneous ideas in a social network [13].”
Missing and spurious interactions and the reconstruction of complex networks (2009, background): “First, nodes in real networks are often organized into modules or communities [15, 16], which may overlap [17] or be hie rarchically nested [18, 19, 11], so that connections are relati vely more abundant within modules than between modules.”
Community detection in graphs (2009, background): “Interestingly, Arenas et al. found that the structural scales revealed by synchronization correspond to groups of eigenvalues of the Laplacian matrix of the graph, separated by gaps (Fig.”
Synchronization in complex networks (2008, methodology): “The method is closely related to the determination of community structure via synchronization processes devised by several authors (Arenas et al., 2006b; Boccaletti et al., 2007).”