# Modeling Graphs with Vertex Replacement Grammars

## TL;DR

This paper introduces a revised vertex replacement grammar, CNRG, which efficiently models large graphs by capturing their hierarchical structure, enabling realistic graph generation that preserves original network properties.

## Contribution

It presents a novel variant of VRG called CNRG, capable of extracting hierarchical graph models from large datasets, improving upon previous limitations of graph grammar formalisms.

## Key findings

- CNRGs can be efficiently extracted from hierarchical clusterings.
- Graphs generated from CNRGs resemble original networks in properties.
- CNRGs provide a succinct yet faithful graph representation.

## Abstract

One of the principal goals of graph modeling is to capture the building blocks of network data in order to study various physical and natural phenomena. Recent work at the intersection of formal language theory and graph theory has explored the use of graph grammars for graph modeling. However, existing graph grammar formalisms, like Hyperedge Replacement Grammars, can only operate on small tree-like graphs. The present work relaxes this restriction by revising a different graph grammar formalism called Vertex Replacement Grammars (VRGs). We show that a variant of the VRG called Clustering-based Node Replacement Grammar (CNRG) can be efficiently extracted from many hierarchical clusterings of a graph. We show that CNRGs encode a succinct model of the graph, yet faithfully preserves the structure of the original graph. In experiments on large real-world datasets, we show that graphs generated from the CNRG model exhibit a diverse range of properties that are similar to those found in the original networks.