Graph neural networks have received increased attention over the past years due to their promising ability to handle graph-structured data, which can be found in many real-world problems such as recommended systems and drug synthesis. Most existing research focuses on using graph neural networks to solve homophilous problems, but little attention has been paid to heterophily-type problems. In this paper, we propose a graph network model for graph coloring, which is a class of representative heterophilous problems. Different from the conventional graph networks, we introduce negative message passing into the proposed graph neural network for more effective information exchange in handling graph coloring problems. Moreover, a new loss function taking into account the self-information of the nodes is suggested to accelerate the learning process. Experimental studies are carried out to compare the proposed graph model with five state-of-the-art algorithms on ten publicly available graph coloring problems and one real-world application. Numerical results demonstrate the effectiveness of the proposed graph neural network.

翻译：近年来，图神经网络因在处理图结构数据（如推荐系统和药物合成等现实问题中常见的数据形式）方面的显著能力而受到越来越多的关注。现有研究大多集中于利用图神经网络解决同质性问题，而对异质型问题的关注较少。本文针对图着色这一代表性异质问题，提出了一种图网络模型。与传统图网络不同，我们在这款图神经网络中引入了负消息传递机制，以更有效地进行图着色问题中的信息交换。此外，我们提出了一种考虑节点自信息的新损失函数，以加速学习过程。通过实验研究，我们在十个公开图着色问题和一个实际应用场景中，将所提出图模型与五种最先进算法进行了比较。数值结果验证了所提出图神经网络的有效性。