Towards Interpretable Graph Modeling with Vertex Replacement Grammars

TL;DR

This paper introduces KT grammars, a new type of vertex replacement grammar derived using MDL, which effectively captures interpretable patterns and dynamics in real-world graph data.

Contribution

It proposes a novel KT grammar framework for interpretable graph modeling based on MDL, addressing limitations of previous graph grammar approaches.

Findings

KT grammars can be efficiently extracted from graphs

They encode meaningful, interpretable patterns

Effective on synthetic and real-world datasets

Abstract

An enormous amount of real-world data exists in the form of graphs. Oftentimes, interesting patterns that describe the complex dynamics of these graphs are captured in the form of frequently reoccurring substructures. Recent work at the intersection of formal language theory and graph theory has explored the use of graph grammars for graph modeling and pattern mining. However, existing formulations do not extract meaningful and easily interpretable patterns from the data. The present work addresses this limitation by extracting a special type of vertex replacement grammar, which we call a KT grammar, according to the Minimum Description Length (MDL) heuristic. In experiments on synthetic and real-world datasets, we show that KT-grammars can be efficiently extracted from a graph and that these grammars encode meaningful patterns that represent the dynamics of the real-world system.