We propose a novel model for generating graphs similar to a given example
graph. Unlike standard approaches that compute features of graphs in Euclidean
space, our approach obtains features on a surface of a hypersphere. We then
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 a popular exponential random graph model
(ERGM), unlike ERGMs, it does not suffer from degeneracy, a situation when a
significant 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 the small domain of all 8-node graphs as well as larger real-world social
networks.Comment: 29 pages, 14 figures, 1 tabl