Size Matters: Large Graph Generation with HiGGs
Keywords: Graph-based Learning, Deep Learning, (Application) Social Networks
TL;DR: GNNs conditioning GNNs, in hierarchies of graph-resolution, allows HiGGs to produce graphs with tens of thousands of attributed nodes - far larger than currently possible.
Abstract: Large graphs are present in a variety of domains, including social networks, civil
infrastructure, and the physical sciences to name a few. Graph generation is
similarly widespread, with applications in drug discovery, network analysis and
synthetic datasets among others. While GNN (Graph Neural Network) models
have been applied in these domains their high in-memory costs restrict them to
small graphs. Conversely less costly rule-based methods struggle to reproduce
complex structures. We propose HIGGS (Hierarchical Generation of Graphs)
as a model-agnostic framework of producing large graphs with realistic local
structures. HIGGS uses GNN models with conditional generation capabilities to
sample graphs in hierarchies of resolution. As a result HIGGS has the capacity
to extend the scale of generated graphs from a given GNN model by quadratic
order. As a demonstration we implement HIGGS using DiGress, a recent graph-
diffusion model, including a novel edge-predictive-diffusion variant edge-DiGress.
We use this implementation to generate categorically attributed graphs with tens
of thousands of nodes. These HIGGS generated graphs are far larger than any
previously produced using GNNs. Despite this jump in scale we demonstrate that
the graphs produced by HIGGS are, on the local scale, more realistic than those
from the rule-based model BTER.
Submission Number: 9
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