Learning Hyperedge Replacement Grammars for Graph Generation

TL;DR

This paper introduces a novel method for learning hyperedge replacement grammars from clique trees to generate realistic graphs that preserve both global properties and local substructures, advancing graph modeling techniques.

Contribution

The work presents a new approach to extract HRGs from clique trees for graph generation, capturing both global and local network features.

Findings

Generated graphs match original network properties

Preserves local substructures in new graphs

Effective on large real-world networks

Abstract

The discovery and analysis of network patterns are central to the scientific enterprise. In the present work, we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate new realistic graphs. Our key insight is that a graph's clique tree encodes robust and precise information. We show that a Hyperedge Replacement Grammar (HRG) can be extracted from the clique tree, and we develop a fixed-size graph generation algorithm that can be used to produce new graphs of a specified size. In experiments on large real-world graphs, we show that graphs generated from the HRG approach exhibit a diverse range of properties that are similar to those found in the original networks. In addition to graph properties like degree or eigenvector centrality, what a graph "looks like" ultimately depends on small details in local graph substructures that are difficult to define at a global level. We show that the HRG model can also preserve these local substructures when generating new graphs.