Conservative vs. non-conservative diffusion towards a target in a networked environment

The networked nature of complex systems determines the way in which
’information’ navigates the system from a source to a target. This navigation is governed
by the lack of central controllers and the fact that every individual entity ignores
the global structure of the system. Consequently, targeted shortest-path searches are
almost automatically excluded in these systems, leaving the more blind diffusive
processes as the main mechanism for navigating complex networks. Here we show
that non-conservative diffusion has some advantages over the ’classical’ (conservative)
diffusion for searching a target in a network. The non-conservative nature of the
diffusion process is given by the possibility that the network ’communicates’ with the
environment in which it is embedded.We use analytical and computational methods
to show that non-conservative diffusion uses trajectories which are more prone to
find a target than the conservative one.We illustrate the existence of this mechanisms
in systems as varied as traffic in urban environments, volume transmission in the
brain and communication through online social networks.