Attributed Graph Modeling with Vertex Replacement Grammars

Abstract: Recent work at the intersection of formal language theory and graph theory has explored graph grammars for graph modeling. However, existing models and formalisms can only operate on homogeneous (i.e., untyped or unattributed) graphs. We relax this restriction and introduce the Attributed Vertex Replacement Grammar (AVRG), which can be efficiently extracted from heterogeneous (i.e., typed, colored, or attributed) graphs. Unlike current state-of-the-art methods, which train enormous models over complicated deep neural architectures, the AVRG model is unsupervised and interpretable. It is based on context-free string grammars and works by encoding graph rewriting rules into a graph grammar containing graphlets and instructions on how they fit together. We show that the AVRG can encode succinct models of input graphs yet faithfully preserve their structure and assortativity properties. Experiments on large real-world datasets show that graphs generated from the AVRG model exhibit substructures and attribute configurations that match those found in the input networks.