Hubs-attracting Laplacian and related synchronization on networks. (English) Zbl 1439.05210
Summary: In this work, we introduce a new Laplacian matrix, referred to as the hubs-attracting Laplacian, 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, 256–280 (2020; Zbl 1435.05127)], 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.
MSC:
| 05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C90 | Applications of graph theory |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
Citations:
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