  Communication of signals among nodes in a complex network poses fundamental
problems of efficiency and cost. Routing of messages along shortest paths
requires global information about the topology, while spreading by diffusion,
which operates according to local topological features, is informationally
"cheap" but inefficient. We introduce a stochastic model for network
communication that combines varying amounts of local and global information
about the network topology. The model generates a continuous spectrum of
dynamics that converge onto shortest-path and random-walk (diffusion)
communication processes at the limiting extremes. We implement the model on two
cohorts of human connectome networks and investigate the effects of varying
amounts of local and global information on the network's communication cost. We
identify routing strategies that approach a (highly efficient) shortest-path
communication process with a relatively small amount of global information.
Moreover, we show that the cost of routing messages from and to hub nodes
varies as a function of the amount of global information driving the system's
dynamics. Finally, we implement the model to identify individual subject
differences from a communication dynamics point of view. The present framework
departs from the classical shortest paths vs. diffusion dichotomy, suggesting
instead that brain networks may exhibit different types of communication
dynamics depending on varying functional demands and the availability of
resources.
