2020/03/02 by Sarika Jalan, Priodyuti Pradhan
Neuroscience · Physics and Astronomy · #Centrality #Complex Network Analysis Techniques #Complex network #Construct (python library) #Criticality #Eigenvalues and eigenvectors #Functional Brain Connectivity Studies #Graph #Opinion Dynamics and Social Influence #Principal component analysis #Topology (electrical circuits) #nlin.AO #physics.soc-ph
paper · pdf · doi:10.1209/0295-5075/129/46002
published as EPL (Europhysics Letters), 129(4), 46002 (2020) · 6 pages, 5 figures
arxiv created 2020/03/02 · openalex created_date 2020/03/13 · openalex publication_date 2020/03/23 · arxiv updated 2020/04/08 · openalex updated_date 2026/08/05
Investigation of eigenvector localization properties of complex networks is not only important for gaining insight into fundamental network problems such as network centrality measure, spectral partitioning, development of approximation algorithms, but is also crucial for understanding many real-world phenomena such as disease spreading, criticality in brain network dynamics. For a network, an eigenvector is said to be localized when most of its components take value near to zero, with a few components taking very high values. In this article, we devise a methodology to construct a principal eigenvector (PEV) localized network from a given input network. The methodology relies on adding a small component having a wheel graph to the given input network. By extensive numerical simulation and an analytical formulation based on the largest eigenvalue of the input network, we compute the size of the wheel graph required to localize the PEV of the combined network. Using the susceptible-infected-susceptible model, we demonstrate the success of this method for various models and real-world networks considered as input networks. We show that on such PEV localized networks, the disease gets localized within a small region of the network structure before the outbreaks. The study is relevant in controlling spreading processes on complex systems represented by networks.