While Graph Neural Networks (GNNs) have made significant strides in diverse areas, they are hindered by a theoretical constraint known as the 1-Weisfeiler-Lehmann test. Even though latest advancements in higher-order GNNs can overcome this boundary, they typically center around certain graph components like cliques or cycles. However, our investigation goes a different route. We put emphasis on paths, which are inherent in every graph. We are able to construct a more general topological perspective and form a bridge to certain established theories about other topological domains. Interestingly, without any assumptions on graph sub-structures, our approach surpasses earlier techniques in this field, achieving state-of-the-art performance on several benchmarks.

图神经网络在各个领域取得了显著进展, 但受到称为1-Weisfeiler-Lehmann测试的理论约束. 尽管最新的高阶图神经网络可以克服这个限制, 但它们通常集中于某些图的组成要素，如团或环. 然而, 我们的研究选择了一条不同的路线, 侧重于路径, 这在任何图中都是固有的. 我们能够构建一个更一般的拓扑视角，并将它与其他拓扑领域的一些已有理论建立联系. 有趣的是, 在不对图的子结构作出任何假设的情况下, 我们的方法在该领域超过早期的技术，达到了几个基准上的最先进性能.

推广路径拓扑图神经网络