Synchronous Hyperedge Replacement Graph Grammars

Abstract

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. Recent work at the intersection of formal language theory and graph theory has found that a Probabilistic Hyperedge Replacement Grammar (PHRG) can be extracted from a tree decomposition of any graph. However, because the extracted PHRG is directly dependent on the shape and contents of the tree decomposition, rather than from the dynamics of the graph, it is unlikely that informative graph-processes are actually being captured with the PHRG extraction algorithm. To address this problem, the current work adapts a related formalism called Probabilistic Synchronous HRG (PSHRG) that learns synchronous graph production rules from temporal graphs. We introduce the PSHRG model and describe a method to extract growth rules from the graph. We find that SHRG rules capture growth patterns found in temporal graphs and can be used to predict the future evolution of a temporal graph. We perform a brief evaluation on small synthetic networks that demonstrate the prediction accuracy of PSHRG versus baseline and state of the art models. Ultimately, we find that PSHRGs seem to be very good at modelling dynamics of a temporal graph; however, our prediction algorithm, which is based on string parsing and generation algorithms, does not scale to practically useful graph sizes.