Generative models for graphs have been typically committed to strong prior
assumptions concerning the form of the modeled distributions. Moreover, the
vast majority of currently available models are either only suitable for
characterizing some particular network properties (such as degree distribution
or clustering coefficient), or they are aimed at estimating joint probability
distributions, which is often intractable in large-scale networks. In this
paper, we first propose a novel network statistic, based on the Laplacian
spectrum of graphs, which allows to dispense with any parametric assumption
concerning the modeled network properties. Second, we use the defined statistic
to develop the Fiedler random graph model, switching the focus from the
estimation of joint probability distributions to a more tractable conditional
estimation setting. After analyzing the dependence structure characterizing
Fiedler random graphs, we evaluate them experimentally in edge prediction over
several real-world networks, showing that they allow to reach a much higher
prediction accuracy than various alternative statistical models.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty
in Artificial Intelligence (UAI2012
