Bounding network spectra for network design

Abstract

The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation between the eigenvalues of weighted and unweighted networks, here I show that for a wide class of networks the dynamical behavior is tightly bounded by few network parameters. This result provides rigorous conditions for the design of networks with predefined dynamical properties and for the structural control of physical processes in complex systems. The results are illustrated using synchronization phenomena as a model process.

17 pages, 4 figures

References in corpus (32)

• Emergence of scaling in random networks
• The architecture of complex weighted networks
• Random graphs with arbitrary degree distributions and their applications
• Synchronization in small-world systems
• Synchronization reveals topological scales in complex networks
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Scale-Free Networks are Ultrasmall
• 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
• Generic scale of the "scale-free" growing networks
• Spectra of complex networks
• Synchronization of Kuramoto Oscillators in Scale-Free Networks
• Spectral Properties and Synchronization in Coupled Map Lattices
• Characterizing the dynamical importance of network nodes and links
• Synchronization is optimal in non-diagonalizable networks
• Maximum Performance at Minimum Cost in Network Synchronization
• Random Delays and the Synchronization of Chaotic Maps
• Self-organized and driven phase synchronization in coupled maps
• Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that
• Breaking Synchrony by Heterogeneity in Complex Networks
• Coherence in scale-free networks of chaotic maps
• Uncorrelated Random Networks
• Designing the Dynamics of Spiking Neural Networks
• Synchronization transition of heterogeneously coupled oscillators on scale-free networks
• Dynamics on Complex Networks and Applications
• Trading interactions for topology in scale-free networks
• Designing Complex Networks
• Weighted networks are more synchronizable: how and why
• Periodic Neural Activity Induced by Network Complexity

Cited by in corpus (18)

• Critical phenomena in complex networks
• Random walks and diffusion on networks
• Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions
• Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?
• Enhancing the spectral gap of networks by node removal
• Does the brain behave like a (complex) network? I. Dynamics
• Network synchronizability analysis: the theory of subgraphs and complementary graphs
• Network Coordination and Synchronization in a Noisy Environment with Time Delays
• Network synchronization: Optimal and Pessimal Scale-Free Topologies
• Functional control of network dynamics using designed Laplacian spectra
• Rewiring hierarchical scale-free networks: Influence on synchronizability and topology
• Network evolution towards optimal dynamical performance
• Symmetry-based coarse-graining of evolved dynamical networks
• Isospectral Graph Reductions
• Probability of Stability of Synchronization in Random Networks of Mismatched Oscillators
• Synchronization in Networks of Identical Systems via Pinning: Application to Distributed Secondary Control of Microgrids
• Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra
• Stability Analysis of Network of Similar-Plants via Feedback Network