Asymmetric Distribution of Nodes in the Spatial Preferred Attachment Model

In this paper, a spatial preferential attachment model for complex networks in which there is non-uniform distribution of the nodes in the metric space is studied. In this model, the metric layout represents hidden information about the similarity and community structure of the nodes. It is found that, for density functions that are locally constant, the graph properties can be well approximated by considering the graph as a union of graphs from uniform density spatial models corresponding to the regions of different densities. Moreover, methods from the uniform case can be used to extract information about the metric layout. Specifically, through link and co-citation analysis the density of a node’s region can be estimated and the pairwise distances for certain nodes can be recovered with good accuracy.