Some Typical Properties of the Spatial Preferred Attachment Model

Abstract We investigate a stochastic model for complex networks, based on a spatial embedding of the nodes, called the spatial preferred attachment (SPA) model. In the SPA model, nodes have spheres of influence of varying sizes, and a new node may link to a node only if it falls within its region of influence. The spatial embedding of the nodes models the background knowledge or identity of the node, which influences its link environment. In this paper, we focus on the (directed) diameter, small separators, and the (weak) giant component of the model.