Structural and functional properties of spatially embedded scale-free networks.

Scale-free networks have been studied mostly as non-spatially embedded systems. However, in many realistic cases, they are spatially embedded and these constraints should be considered. Here, we study the structural and functional properties of a model of scale-free (SF) spatially embedded networks.

Diffusion, annihilation, and chemical reactions in complex networks with spatial constraints.

We consider Erdö]s-Rényi-type networks embedded in one-dimensional (de=1) and two-dimensional (de=2) Euclidean space with the link-length distribution p(r)∼r-δ. The dimension d of these networks, as a function of δ, has been studied earlier and has been shown to depend on δ. Here we consider diffusion, annihilation, and chemical reaction processes on these spatially constrained networks and show that their dynamics is controlled by the dimension d of the system.