We present a graph bisection and partitioning algorithm based on graph neural networks. For each node in the graph, the network outputs probabilities for each of the partitions. The graph neural network consists of two modules: an embedding phase and a partitioning phase. The embedding phase is trained first by minimizing a loss function inspired by spectral graph theory. The partitioning module is trained through a loss function that corresponds to the expected value of the normalized cut. Both parts of the neural network rely on SAGE convolutional layers and graph coarsening using heavy edge matching. The multilevel structure of the neural network is inspired by the multigrid algorithm. Our approach generalizes very well to bigger graphs and has partition quality comparable to METIS, Scotch and spectral partitioning, with shorter runtime compared to METIS and spectral partitioning.

翻译：我们根据图形神经网络提供一个基于图形神经网络的图形分解和分区算法。 对于图形中的每个节点, 每一个分区的网络输出概率。 图形神经网络由两个模块组成: 嵌入阶段和分区阶段。 嵌入阶段首先通过最大限度地减少光谱图形理论所激发的损失函数来培训。 分割单元通过一个与正常切分的预期值相对应的损失函数来培训。 神经网络的两个部分都依赖于SAGE 相向层和使用重边缘匹配的图形粗化。 神经网络的多层次结构受多格算法的启发。 我们的方法非常接近较大的图形, 并且具有与METIS、 苏格兰和光谱分割法相近的分布质量。 与MEDIS 和光谱分割相比, 运行时间较短 。