Competition and cooperation between active intra-network and passive extra-network transport processes

Many networks are embedded in physical space and often interact with it. This interaction can be exemplified through constraints exerted on network topology, or through interactions of processes defined on a network with those that are linked to the space that the network is embedded within, leading to complex dynamics. Here we discuss an example of such an interaction in which a signaling agent is actively transported through the network edges and, at the same time, spreads passively through space due to diffusion. We show that these two processes cooperate or compete depending on the network topology leading to complex dynamics.