Non-local network dynamics via fractional graph Laplacians

被引：17

作者：

Benzi, Michele ^{[1
]}

Bertaccini, Daniele ^{[2
,3
]}

Durastante, Fabio ^{[3
]}

Simunec, Igor ^{[1
]}

机构：

[1] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy

[2] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci 1, I-00133 Rome, Italy

[3] CNR, Ist Applicaz Calcolo M Picone, Via Pietro Castellino 111, I-80131 Rome, Italy

来源：

JOURNAL OF COMPLEX NETWORKS | 2020年 / 8卷 / 03期

关键词：

network dynamics; non-local dynamics; superdiffusion; matrix functions; power law decay; DECAY BOUNDS; MATRICES;

D O I：

10.1093/comnet/cnaa017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：29

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