Paper Info
Title
Hubs-attracting Laplacian and Related Synchronization on Networks
Abstract
In this work, we introduce a new Laplacian matrix, referred to as the hubs-attracting La placian, accounting for diffusion processes on networks where the hopping of a particle occurs with higher probability from low to high degree nodes. This notion complements the one of the hubs-repelling Laplacian discussed in [E. Estrada, Linear Algebra Appl., 596 (2020), pp. 256-280], that considers the opposite scenario, with higher hopping probabilities from high to low degree nodes. We formulate a model of oscillators coupled through the new Laplacian and study the synchronizability of the network through the analysis of the spectrum of the Laplacian. We discuss analytical results providing bounds for the quantities of interest for synchronization and computational results showing that the hubs-attracting Laplacian generally has better synchronizability properties when compared to the classical one, with a low occurrence rate for the graphs where this is not true. Finally, two illustrative case studies of synchronization through the hubs-attracting Laplacian are considered.
Year
DOI
Venue
2020
10.1137/19M1287663
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Keywords
DocType
Volume
Laplacian matrix,networks of coupled dynamical systems,synchronization
Journal
19
Issue
ISSN
Citations 
2
1536-0040
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Lucia Valentina Gambuzza1546.94
Mattia Frasca231360.35
Ernesto Estrada3218.85