Small-world spectra in mean field theory
arXiv:1112.1728 · doi:10.1103/PhysRevLett.108.218701
Abstract
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions agree well with the actual spectra (obtained by numerical diagonalization) for undirected and directed networks and from fully regular to strongly random topologies. These results may provide analytical insights to empirically found features of dynamics on small-world networks from various research fields, including biology, physics, engineering and social science.
5 pages, 4 figures
References in corpus (4)
Cited by in corpus (16)
- The Kuramoto model in complex networks
- Nonnormal amplification in random balanced neuronal networks
- Eigenvalues of normalized Laplacian matrices of fractal trees and dendrimers: Analytical results and applications
- Collective Relaxation Dynamics of Small-World Networks
- Universality in the spectral and eigenfunction properties of random networks
- Heterogeneous continuous time random walks
- Complex Quantum Networks: From Universal Breakdown to Optimal Transport
- Spectra of Random Stochastic Matrices and Relaxation in Complex Systems
- Erosion of synchronization: Coupling heterogeneity and network structure
- Collective frequency variation in network synchronization and reverse PageRank
- Scaling Laws in Spatial Network Formation
- Dynamics of "comb-of-comb" networks
- An ensemble perspective on multi-layer networks
- Adhesion-induced Discontinuous Transitions and Classifying Social Networks
- Structural and temporal heterogeneities on networks
- Diffusion dynamics and synchronizability of hierarchical products of networks