Characterizing the structure of small-world networks
E. Almaas, R. V. Kulkarni, D. Stroud
Abstract
We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be used to obtain approximations for the corresponding basic probability distribution. In the limit of large system sizes and small disorder, we use numerical studies to obtain a functional fit for this distribution. Finally, we obtain the scaling properties for the mean-square displacement of a random walker, which are determined by the scaling behavior of the underlying SWN.
Create a lesson
Related papers
Cell-type-specific modularity in E/I networks shapes dynamical regimes and computational capabilities
Emmanouil Giannakakis, Victor Buendía, Oleg Vinogradov et al.
Finite-width shift of the edge of chaos in deep neural networks
Arn Caesar
Neural Networks with Exciton-Polariton Waveguides
Huawen Xu, Ruiqi Bao, Lingyu Tian et al.
Optical Ceiling on Polaron Mobility in Disordered Molecular Semiconductors: Lessons from Eumelanin
Alvan Hunt
Glauber dynamics of the Sherrington--Kirkpatrick spin-glass model: a dynamical cavity method
Grzegorz Szamel
Generative diffusion in long-range correlated landscapes: Speciation cascade and the foam structure of the score
Jerome Garnier-Brun, Giulio Biroli, Marc Mézard et al.