Diffusion and networks: A powerful combination!

Abstract

Over the last decade, an enormous interest and activity in complex networks have been witnessed within the physics community. On the other hand, diffusion and its theory, have equipped the toolbox of the physicist for decades. In this paper, we will demonstrate how to combine these two seemingly different topics in a fruitful manner. In particular, we will review and develop further, an auxiliary diffusive process on weighted networks that represents a powerful concept and tool for studying network (community) structures. The working principle of the method is the observation that the relaxation of the diffusive process towards the stationary state is {\em non-local} and fastest in the highly connected regions of the network. This can be used to acquire non-trivial information about the structure of clustered and non-clustered networks.