Deep Learning Chromatic and Clique Numbers of Graphs

TL;DR

This paper develops deep learning models, especially convolutional neural networks, to predict the chromatic number and maximum clique size of graphs directly from adjacency matrices, addressing classical NP-complete problems.

Contribution

It introduces a novel approach of using deep neural networks with minimal graph representation to predict complex graph invariants, demonstrating strong empirical performance.

Findings

Neural networks accurately predict chromatic numbers and clique sizes.

Convolutional neural networks outperform traditional methods.

Minimal graph representation suffices for effective learning.

Abstract

Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine learning community. In this work, we develop deep learning models to predict the chromatic number and maximum clique size of graphs, both of which represent classical NP-complete combinatorial optimization problems encountered in graph theory. The neural networks are trained using the most basic representation of the graph, the adjacency matrix, as opposed to undergoing complex domain-specific feature engineering. The experimental results show that deep neural networks, and in particular convolutional neural networks, obtain strong performance on this problem.