2020/10/18 by Ankit Mishra, Jayendra N. Bandyopadhyay, Sarika Jalan · 8 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Adjacency list #Adjacency matrix #Average path length #Cluster analysis #Combinatorics #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Complex network #Computer science #Dimension (graph theory) #Eigenvalues and eigenvectors #Fractal #Mathematical analysis #Mathematics #Multifractal system #Nonlinear Dynamics and Pattern Formation #Path (computing) #Path length #Physics #Quantum mechanics #Shortest path problem #Small-world network #Spectrum (functional analysis) #Statistics #Topology (electrical circuits) #cond-mat.dis-nn #physics.soc-ph
paper · pdf · doi:10.1016/j.chaos.2021.110745
published in Chaos Solitons & Fractals 144, 110745 (Elsevier BV) · 8 pages, 7 figures
arxiv created 2020/10/18 · openalex publication_date 2021/02/10 · arxiv updated 2021/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths.It is well-known that higher clustering drives localization while shorter path length supports delocalization of the eigenvectors of networks. Using multifractals technique, we investigate localization properties of the eigenvectors of the adjacency matrices of small-world networks constructed using Watts-Strogatz algorithm. We find that the central part of the eigenvalue spectrum is characterized by strong multifractality whereas the tail part of the spectrum have Dq->1. Before the onset of the small-world transition, an increase in the random connections leads to an enhancement in the eigenvectors localization, whereas just after the onset, the eigenvectors show a gradual decrease in the localization. We have verified an existence of sharp change in the correlation dimension at the localization-delocalization transition