Modeling Interstate Alliances with Constrained Random Dot Product Graphs

A new model of random graphs, the random dot product graph (RDPG) is described. This model is well suited to social networks, since it defines the edges in the graph in terms of a vector of “attributes”. The edge probabilities are modeled as the dot product of vectors associated with the vertices. A small set of distinct vectors is used, allowing the automatic grouping of vertices according to their attributes. We discuss various issues of model fitting and model selection for the reduced vector set version of the RDPG. We extend the basic model to model time series of graphs, and illustrate the model through application to a time series of graphs defined by the alliances between nation states.