%0 Journal Article
%T Non-Uniform Distribution of Nodes in the Spatial Preferential Attachment Model
%A Jeannette Janssen
%A Pawel Pralat
%A Rory Wilson
%J Computer Science
%D 2015
%I arXiv
%X The spatial preferential attachment (SPA) is a model for complex networks. In the SPA model, nodes are embedded in a metric space, and each node has a sphere of influence whose size increases if the node gains an in-link, and otherwise decreases with time. In this paper, we study the behaviour of the SPA model when the distribution of the nodes is non-uniform. Specifically, the space is divided into dense and sparse regions, where it is assumed that the dense regions correspond to coherent communities. We prove precise theoretical results regarding the degree of a node, the number of common neighbours, and the average out-degree in a region. Moreover, we show how these theoretically derived results about the graph properties of the model can be used to formulate a reliable estimator for the distance between certain pairs of nodes, and to estimate the density of the region containing a given node.
%U http://arxiv.org/abs/1506.06053v1