Estimating Graph Parameters Using Graph Grammars

Abstract

Stochastic graph grammars are probabilistic models suitable for modeling relational data, complex organic molecules, social networks, and various other data distributions [1]. In this paper, we demonstrate that such grammars can be used to reveal useful information about the underlying distribution. In particular, we demonstrate techniques for estimating the expected number of nodes, the expected number of edges, and the expected average node degree, in a graph sampled from the distribution. These estimation techniques use the underlying grammar, and hence do not require sampling. Experimental results indicate that our estimation techniques are reasonably accurate.