Dynamical and spectral properties of complex networks
arXiv:0705.3216 · doi:10.1088/1367-2630/9/6/187
Abstract
Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of networks and different dynamics. We show that the main dependence of the synchronization time is on the smallest nonzero eigenvalue of the Laplacian matrix, in contrast to other proposals in terms of the spectrum of the adjacency matrix. Then, this topological property becomes the most relevant for the dynamics.
14 pages, 5 figures, to be published in New Journal of Physics
References in corpus (23)
- Emergence of scaling in random networks
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Finding and evaluating community structure in networks
- Evolution of networks
- Comparing community structure identification
- Synchronization in small-world systems
- Renormalization group analysis of the small-world network model
- Synchronization reveals topological scales in complex networks
- Network Synchronization, Diffusion, and the Paradox of Heterogeneity
- Paths to Synchronization on Complex Networks
- Entangled networks, synchronization, and optimal network topology
- Universality in the synchronization of weighted random networks
- Enhancing complex-network synchronization
- Synchronization of Kuramoto Oscillators in Scale-Free Networks
- Characterizing the dynamical importance of network nodes and links
- Synchronization processes in complex networks
- Maximum Performance at Minimum Cost in Network Synchronization
- Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that
- Fitness for Synchronization of Network Motifs
- Sparse repulsive coupling enhances synchronization in complex networks
- Synchronization Properties of Network Motifs
- Dynamics on Complex Networks and Applications
Cited by in corpus (38)
- Synchronization in complex networks
- Diffusion dynamics on multiplex networks
- Spectral properties of the Laplacian of multiplex networks
- Temporal networks: slowing down diffusion by long lasting interactions
- Spectral and Dynamical Properties in Classes of Sparse Networks with Mesoscopic Inhomogeneities
- Defining a historic football team: Using Network Science to analyze Guardiola's F.C. Barcelona
- Eigenvalue Spectra of Modular Networks
- Emergent stability in complex network dynamics
- Dimensionality reduction and spectral properties of multilayer networks
- Optimal Network Topology for Effective Collective Response
- Diffusion Dynamics and Optimal Coupling in Directed Multiplex Networks
- Enhancing the spectral gap of networks by node removal
- Hidden Symmetries in Real and Theoretical Networks
- Does the brain behave like a (complex) network? I. Dynamics
- Synchronization in Random Geometric Graphs
- Network Reliability: The effect of local network structure on diffusive processes
- Nonautonomous driving induces stability in network of identical oscillators
- A generative model for protein contact networks
- Optimal phase synchronization in networks of phase-coherent chaotic oscillators
- Communicability Angles Reveal Critical Edges for Network Consensus Dynamics
- Synchronization on Effective Networks
- Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators
- Analytic relationship of relative synchronizability to network structure and motifs
- Dynamics of "comb-of-comb" networks
- Accelerating coordination in temporal networks by engineering the link order
- Symmetry and localization of quantum walk induced by extra link in cycles
- Graph spectral characterisation of the XY model on complex networks
- Finite-size effects on the convergence time in continuous-opinion dynamics
- Layer degradation triggers an abrupt structural transition in multiplex networks
- Multiple structural transitions in interacting networks
- Influence of cumulative damage on synchronization of Kuramoto oscillators on networks
- Organic Design of Massively Distributed Systems: A Complex Networks Perspective
- Antifragility and response to damage in the synchronization of oscillators on networks
- How to grow an oscillator network with enhanced synchronization
- Nested canalizing functions minimize sensitivity and simultaneously promote criticality
- Reconstruction of evolved dynamic networks from degree correlations
- Spectral properties of unimodular lattice triangulations
- Dynamical leaps due to microscopic changes in multiplex networks