COMPSTAT 2006 August 28 - September 1, 2006 Rome Solicited Session: Modeling and Statistical Inference for Time Series of Graphs Session Organizer: Carey E. Priebe Johns Hopkins University, Baltimore - USA Invited Speakers: # Ed Scheinerman (JHU) # David Marchette (NSWC) # Bill Szewczyk (NSA) ================================================== # Ed Scheinerman (JHU) Dot Product Models of Graphs: A Noneuclidean, Low-Dimensional Approach We present a technique to model graphs in low dimensional space. The method is based on the concept of a random dot product graph in which vertices are represented by vectors and edge probabilities are given by the dot products of these vectors. In our approach, we are presented with a graph (or a time series of graphs, or an edge-weighted graph) and efficiently compute vectors such that the pairwise dot products of these vectors are as near the edge weights as possible. These vectors can then be used to characterize the vertices they represent. ================================================== # David Marchette (NSWC) Time Series of Dot Product Graphs A dot product graph is a random graph in which the edge probabilities are defined by the dot products of vectors associated with the vertices. We consider a constrained version of the dot product graph, in which the number of distinct vectors is constrained to be K