Implicit Graphon Neural Representation

TL;DR

This paper introduces Implicit Graphon Neural Representation (IGNR), a neural network-based method for modeling graphons that can generate graphs of arbitrary size and structure, handling unaligned and varying-sized graph data effectively.

Contribution

The paper presents a novel neural network approach to model graphons directly, enabling high-resolution representation and efficient generation of graphs of arbitrary size, with extensions for auto-encoder integration.

Findings

IGNR outperforms existing graphon approximation methods.

The model effectively handles unaligned and variable-sized graph data.

Extensions demonstrate strong performance in graph representation and generation.

Abstract

Graphons are general and powerful models for generating graphs of varying size. In this paper, we propose to directly model graphons using neural networks, obtaining Implicit Graphon Neural Representation (IGNR). Existing work in modeling and reconstructing graphons often approximates a target graphon by a fixed resolution piece-wise constant representation. Our IGNR has the benefit that it can represent graphons up to arbitrary resolutions, and enables natural and efficient generation of arbitrary sized graphs with desired structure once the model is learned. Furthermore, we allow the input graph data to be unaligned and have different sizes by leveraging the Gromov-Wasserstein distance. We first demonstrate the effectiveness of our model by showing its superior performance on a graphon learning task. We then propose an extension of IGNR that can be incorporated into an auto-encoder framework, and demonstrate its good performance under a more general setting of graphon learning. We also show that our model is suitable for graph representation learning and graph generation.