Graph Summarization as Vertex Classification Task using Graph Neural Networks vs. Bloom Filter

The goal of graph summarization is to represent large graphs in a structured and compact way. A graph summary based on equivalence classes preserves predefined features of each vertex within a k-hop neighborhood, such as the vertex and edge labels. Based on these neighborhood characteristics, the vertex is assigned to an equivalence class. The calculation of the assigned equivalence class must be a permutation invariant operation on the predefined features. This is typically achieved by sorting on the feature values, which is computationally expensive, and subsequently hashing the result. Graph Neural Networks (GNNs) fulfill the permutation invariance requirement. We formulate the problem of graph summarization as a subgraph classification task on the root vertex of the k-hop neighborhood. We adapt different GNN architectures, both based on the popular message-passing protocol and alternative approaches, to perform the structural graph summarization task. We compare different GNNs with a standard multi-layer perceptron (MLP) and Bloom filter as a non-neural method. We consider four popular graph summary models on a large web graph. This resembles challenging multi-class vertex classification tasks with the numbers of classes ranging from 576 to hundreds of thousands. Our results show that the performance of GNNs are close to each other. In three out of four experiments, the non-message-passing Graph-MLP model outperforms the other GNNs. The performance of the standard MLP is extraordinarily good, especially in the presence of many classes. Finally, the Bloom filter outperforms all neural architectures by a large margin, except for the dataset with the fewest number (576) of classes. This is an interesting result, since it sheds light on how well and in which contexts GNNs are suited for graph summarization. Furthermore, it demonstrates the need for considering strong non-neural baselines for standard GNN tasks such as vertex classification.