While graph neural networks (GNNs) have achieved great success in learning from graph-structured data, their reliance on local, pairwise message passing restricts their ability to capture complex, high-order subgraph patterns. leading to insufficient structural expressiveness. Recent efforts have attempted to enhance structural expressiveness by integrating random walk kernels into GNNs. However, these methods are inherently designed for graph-level tasks, which limits their applicability to other downstream tasks such as node classification. Moreover, their fixed kernel configurations hinder the model's flexibility in capturing diverse subgraph structures. To address these limitations, this paper proposes a novel Mixture of Subgraph Experts (MoSE) framework for flexible and expressive subgraph-based representation learning across diverse graph tasks. Specifically, MoSE extracts informative subgraphs via anonymous walks and dynamically routes them to specialized experts based on structural semantics, enabling the model to capture diverse subgraph patterns with improved flexibility and interpretability. We further provide a theoretical analysis of MoSE's expressivity within the Subgraph Weisfeiler-Lehman (SWL) Test, proving that it is more powerful than SWL. Extensive experiments, together with visualizations of learned subgraph experts, demonstrate that MoSE not only outperforms competitive baselines but also provides interpretable insights into structural patterns learned by the model.

In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The information obtained from random walks is converted to anonymous walks to extract the topological features of nodes. In the embedding process of nodes, anonymous walks are used since they capture the topological similarities of connectivities better than random walks. Therefore the obtained embedding vectors have richer information about the underlying connectivity structure. The method is applied to node classification and link prediction tasks. The performance of the proposed algorithm is superior to the state-of-the-art algorithms in the recent literature. Moreover, the extracted information about the connectivity structure of similar networks is used to link prediction and node classification tasks for a completely new graph.

Capturing structural similarity has been a hot topic in the field of network embedding recently due to its great help in understanding the node functions and behaviors. However, existing works have paid very much attention to learning structures on homogeneous networks while the related study on heterogeneous networks is still a void. In this paper, we try to take the first step for representation learning on heterostructures, which is very challenging due to their highly diverse combinations of node types and underlying structures. To effectively distinguish diverse heterostructures, we firstly propose a theoretically guaranteed technique called heterogeneous anonymous walk (HAW) and its variant coarse HAW (CHAW). Then, we devise the heterogeneous anonymous walk embedding (HAWE) and its variant coarse HAWE in a data-driven manner to circumvent using an extremely large number of possible walks and train embeddings by predicting occurring walks in the neighborhood of each node. Finally, we design and apply extensive and illustrative experiments on synthetic and real-world networks to build a benchmark on heterostructure learning and evaluate the effectiveness of our methods. The results demonstrate our methods achieve outstanding performance compared with both homogeneous and heterogeneous classic methods, and can be applied on large-scale networks.

Graph neural networks (GNNs) have achieved tremendous success in graph mining. However, the inability of GNNs to model substructures in graphs remains a significant drawback. Specifically, message-passing GNNs (MPGNNs), as the prevailing type of GNNs, have been theoretically shown unable to distinguish, detect or count many graph substructures. While efforts have been paid to complement the inability, existing works either rely on pre-defined substructure sets, thus being less flexible, or are lacking in theoretical insights. In this paper, we propose GSKN, a GNN model with a theoretically stronger ability to distinguish graph structures. Specifically, we design GSKN based on anonymous walks (AWs), flexible substructure units, and derive it upon feature mappings of graph kernels (GKs). We theoretically show that GSKN provably extends the 1-WL test, and hence the maximally powerful MPGNNs from both graph-level and node-level viewpoints. Correspondingly, various experiments are leveraged to evaluate GSKN, where GSKN outperforms a wide range of baselines, endorsing the analysis.

Graph Convolutional Networks (GCNs) achieved tremendous success by effectively gathering local features for nodes. However, commonly do GCNs focus more on node features but less on graph structures within the neighborhood, especially higher-order structural patterns. However, such local structural patterns are shown to be indicative of node properties in numerous fields. In addition, it is not just single patterns, but the distribution over all these patterns matter, because networks are complex and the neighborhood of each node consists of a mixture of various nodes and structural patterns. Correspondingly, in this paper, we propose Graph Structural-topic Neural Network, abbreviated GraphSTONE, a GCN model that utilizes topic models of graphs, such that the structural topics capture indicative graph structures broadly from a probabilistic aspect rather than merely a few structures. Specifically, we build topic models upon graphs using anonymous walks and Graph Anchor LDA, an LDA variant that selects significant structural patterns first, so as to alleviate the complexity and generate structural topics efficiently. In addition, we design multi-view GCNs to unify node features and structural topic features and utilize structural topics to guide the aggregation. We evaluate our model through both quantitative and qualitative experiments, where our model exhibits promising performance, high efficiency, and clear interpretability.

It is not until recently that graph neural networks (GNNs) are adopted to perform graph representation learning, among which, those based on the aggregation of features within the neighborhood of a node achieved great success. However, despite such achievements, GNNs illustrate defects in identifying some common structural patterns which, unfortunately, play significant roles in various network phenomena. In this paper, we propose GraLSP, a GNN framework which explicitly incorporates local structural patterns into the neighborhood aggregation through random anonymous walks. Specifically, we capture local graph structures via random anonymous walks, powerful and flexible tools that represent structural patterns. The walks are then fed into the feature aggregation, where we design various mechanisms to address the impact of structural features, including adaptive receptive radius, attention and amplification. In addition, we design objectives that capture similarities between structures and are optimized jointly with node proximity objectives. With the adequate leverage of structural patterns, our model is able to outperform competitive counterparts in various prediction tasks in multiple datasets.

The task of representing entire graphs has seen a surge of prominent results, mainly due to learning convolutional neural networks (CNNs) on graph-structured data. While CNNs demonstrate state-of-the-art performance in graph classification task, such methods are supervised and therefore steer away from the original problem of network representation in task-agnostic manner. Here, we coherently propose an approach for embedding entire graphs and show that our feature representations with SVM classifier increase classification accuracy of CNN algorithms and traditional graph kernels. For this we describe a recently discovered graph object, anonymous walk, on which we design task-independent algorithms for learning graph representations in explicit and distributed way. Overall, our work represents a new scalable unsupervised learning of state-of-the-art representations of entire graphs.