  Real world networks have, for a long time, been modelled by scale-free
networks, which have many sparsely connected nodes and a few highly connected
ones (the hubs). However, both in society and in biology, a new structure must
be acknowledged, the fractional networks. These networks are characterized by
the existence of very many long-range connections, display superdiffusion,
L\'{e}vy flights and robustness properties different from the scale-free
networks.
