Power-Law Topology Models with Given Spatial Distribution

Many real networks have power-law topological properties as well as some spatial properties. This paper presents a set of models for such topologies. A coverage area (CA) based model (CAM) is proposed with CA of a node to associate the spatial and topological properties. A heuristic gravity algorithm (ERA) is proposed in the sense that a node with heavier mass has larger CA and with gravity to associate both properties. A probabilistic variant of ERA, PERA, is proposed to model the dynamic evolution mechanism of power law network with specific spatial properties. Analysis and simulation show that these models can generate power-law graphs with given spatial distribution and can be realized easily with good scalability