Machine learning on graph-structured data has attracted high research interest due to the emergence of Graph Neural Networks (GNNs). Most of the proposed GNNs are based on the node homophily, i.e neighboring nodes share similar characteristics. However, in many complex networks, nodes that lie to distant parts of the graph share structurally equivalent characteristics and exhibit similar roles (e.g chemical properties of distant atoms in a molecule, type of social network users). A growing literature proposed representations that identify structurally equivalent nodes. However, most of the existing methods require high time and space complexity. In this paper, we propose VNEstruct, a simple approach, based on entropy measures of the neighborhood's topology, for generating low-dimensional structural representations, that is time-efficient and robust to graph perturbations. Empirically, we observe that VNEstruct exhibits robustness on structural role identification tasks. Moreover, VNEstruct can achieve state-of-the-art performance on graph classification, without incorporating the graph structure information in the optimization, in contrast to GNN competitors.

中文翻译：

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图上结构表示的基于自我的熵测度

由于图神经网络（GNN）的出现，对图结构数据的机器学习吸引了很高的研究兴趣。大多数提出的GNN基于同构节点，即相邻节点具有相似的特征。但是，在许多复杂的网络中，位于图的远处的节点具有相同的结构特征并显示相似的角色（例如，分子中远处的原子的化学性质，社交网络用户的类型）。越来越多的文献提出了确定结构上等效节点的表示形式。但是，大多数现有方法需要很高的时间和空间复杂度。在本文中，我们提出了一种VNEstruct，这是一种基于邻域拓扑的熵度量的简单方法，用于生成低维结构表示，这样既省时又健壮，可以绘制扰动图。根据经验，我们观察到VNEstruct在结构角色识别任务上表现出鲁棒性。此外，与GNN竞争对手相比，VNEstruct可以在图形分类上实现最新的性能，而无需在优化中纳入图形结构信息。