# Non-Uniform Distribution of Nodes in the Spatial Preferential Attachment Model

arXiv: https://arxiv.org/abs/1506.06053 · HTML: https://mlsanity.com/paper/1506.06053/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2015.

## Built on by (most cited first, 1 of 1)

- [Unveiling the Sampling Density in Non-Uniform Geometric Graphs](https://mlsanity.com/paper/2210.08219/) (2022)

## Abstract (arXiv)

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.