We introduce non-local dynamics on directed networks through the construction of a fractional version of a non-symmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both directed and undirected graphs, showing the possibility of exploring the network employing random walks with jumps of arbitrary length. We also provide some examples of the applicability of the proposed dynamics, including consensus over multi-agent systems described by directed networks.

Non-local network dynamics via fractional graph Laplacians

Benzi, Michele
;
Durastante, Fabio;Simunec, Igor
2020

Abstract

We introduce non-local dynamics on directed networks through the construction of a fractional version of a non-symmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both directed and undirected graphs, showing the possibility of exploring the network employing random walks with jumps of arbitrary length. We also provide some examples of the applicability of the proposed dynamics, including consensus over multi-agent systems described by directed networks.
2020
Settore MAT/08 - Analisi Numerica
Settore MATH-05/A - Analisi numerica
Matrix functions; Network dynamics; Non-local dynamics; Power law decay; Superdiffusion;
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/89526
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