Generating Similar Graphs From Spherical Features

We present new insights on model degeneracy and a novel model for generating graphs similar to a given example graph. Unlike standard approaches that compute graph features in Euclidean space, our method obtains features on a surface of a hypersphere. We utilize a von Mises-Fisher distribution, an exponential family distribution on the surface of a hypersphere, to define a model over possible feature values. While our approach bears similarity to popular exponential random graph models (ERGMs), unlike ERGMs, it is not prone to degeneracy, a situation when most probability mass is placed on unrealistic graphs. We propose a parameter estimation approach for our model, and a procedure for drawing samples from the distribution. We evaluate the performance of our approach both on a small domain of all 8-node graphs as well as larger real-world social networks.