Properties of the spatial preferential attachment model

This work is a study of the Spatial Preferential Attachment (SPA) Model, a geometric random graph model for complex networks. Geometric models differ from standard models in that the nodes are placed in a space with a metric that defines a distance for each pair of nodes. The distance then affects the link structure.;We determine the expected in-degrees of the nodes in the SPA Model, allowing us to study other geometric properties, specifically edge length added per time step, number of long edges and common neighbours given distance. We look at reverse engineering, determining geometry based on link structure, an idea with great potential for applications.;Lastly, we compare the model to a real-world example, the Enron email dataset, and a good fit is seen.;Key words: Graph theory, geometric graph models, preferential attachment, complex networks, web graph, Spatial Preferential Attachment Model, Enron.