## Internet Mathematics

### A Spatial Web Graph Model with Local Influence Regions

#### Abstract

We present a new 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 influence regions of varying size, and new nodes may link to a node only if they fall within its influence region. The spatial embedding of the nodes models the background knowledge or identity of the node, which will influence its link environment. In our model, nodes can determine their link environment based only on local knowledge of the network. We prove that our model gives a power-law in-degree distribution, with exponent in $[2,\infty)$ depending on the parameters, and with concentration for a wide range of in-degree values.

#### Article information

Source
Internet Math., Volume 5, Number 1-2 (2008), 175-193.

Dates
First available in Project Euclid: 25 November 2009