Current models for complex networks mainly aim to reproduce a number of graph properties observed in real-world networks. On the other hand, experimental and heuristic treatmetns of real-life networks operate under the tacit assumption that the network is a visible manifestation of an underlying hidden reality. For example, it is commonly assumed that communities in a social network can be recognized as densely linked subgraphs, or that Web pages with many common neighbours contain related topics. Such assumptions apply that there is an a priori "community structure" or "relatedness measure" of the nodes, which is reflected by the link structure of the graph.
A common method to represent "relatedness" of objects is by an embedding in a metric space, so that related objects are placed close together, and communities are represented by clusters of points. In this talk, I will discuss graph models where the nodes correspond to points in space, and the stochastic process forming the graph is influenced by the position of the nodes in the space.
The work presented was done in collaboration with Bill Aiello, Anthony Bonato, Colin Cooper, and Pawel Pralat.