Fractional networks, the new structure

TL;DR

This paper introduces fractional networks, a new network structure characterized by many long-range connections, superdiffusion, and different robustness properties, contrasting with traditional scale-free network models.

Contribution

It proposes the concept of fractional networks, highlighting their unique properties and differences from scale-free networks in modeling real-world complex systems.

Findings

Fractional networks exhibit superdiffusion and Lévy flights.

They have distinct robustness properties from scale-free networks.

Long-range connections are prevalent in fractional networks.

Abstract

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.