Algorithm

World Wide Web

Discrete mathematics

Statistics

Dynamics (music)

Laplace operator

Undirected graph

Theoretical computer science

Random graph

Computer science

Acoustics

Complex network

Physics

Graph

Mathematics

Mathematical analysis

Network dynamics

Combinatorics

Directed graph

Topology (electrical circuits)

Laplacian matrix

Fractional Laplacian

Random walk

Journal of Complex Networks

We introduce nonlocal dynamics on directed networks through the construction of a fractional version of a nonsymmetric 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