Lovász Principle for Unsupervised Graph Representation Learning

This paper focuses on graph-level representation learning that aims to represent graphs as vectors that can be directly utilized in downstream tasks such as graph classification. We propose a novel graph-level representation learning principle called Lovász principle, which is motivated by the Lovász number in graph theory. The Lovász number of a graph is a real number that is an upper bound for graph Shannon capacity and is strongly connected with various global characteristics of the graph. Specifically, we show that the handle vector for computing the Lovász number is potentially a suitable choice for graph representation, as it captures a graph's global properties, though a direct application of the handle vector is difficult and problematic. We propose to use neural networks to address the problems and hence provide the Lovász principle. Moreover, we propose an enhanced Lovász principle that is able to exploit the subgraph Lovász numbers directly and efficiently. The experiments demonstrate that our Lovász principles achieve competitive performance compared to the baselines in unsupervised and semi-supervised graph-level representation learning tasks. The code of our Lovász principles is publicly available on GitHub.