Priority diffusion model in lattices and complex networks.

We introduce a model for diffusion of two classes of particles (A and B ) with priority: where both species are present in the same site the motion of A's takes precedence over that of B's. This describes realistic situations in wireless and communication networks. In regular lattices the diffusion of the two species is normal, but the B particles are significantly slower due to the presence of the A particles. From the fraction of sites where the B particles can move freely, which we compute analytically, we derive the diffusion coefficients of the two species. In heterogeneous networks the fraction of sites where B's are free decreases exponentially with the degree of the sites. This, coupled with accumulation of particles in high-degree nodes, leads to trapping of the low priority particles in scale-free networks.