  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.
