Network alignment is a fundamental problem in various domains since it can establish bridges for the same entity (i.e., anchor nodes) between different networks. Most existing network alignment methods are based on consistency assumption, i.e., anchor nodes exhibit similar local structures or neighbors across different networks. However, many anchor nodes have different local structures or neighbors across different networks, which could be regarded as anchor nodes' heterogeneity. It poses a challenge to methods based on the assumption of consistency, as they lack abundant shared information, such as common neighbors. Fortunately, network communities provide the comprehension of node relationships and group structures within networks, which could alleviate the information insufficient. In this article, we propose to address the challenge of inadequate shared information triggered by nodes' heterogeneity from a community perspective. Our model is based on joint optimization of node representation learning and community discovery, including: 1) a node-level constraint is employed to bring nodes with more anchor pairs as neighbors closer together and 2) a community-level constraint is utilized to bring nodes with higher order similarity closer together. We model the cross-network community alignment relations as asymmetric to mitigate the interference caused by anchor node heterogeneity when measuring community alignment relations. Furthermore, we leverage the learned cross-network community alignment relations to supplement node alignment, which could narrow down the search range of potential anchor nodes by focusing solely on aligning nodes within aligned cross-network communities. We conducted extensive experiments on real-world datasets, and the results show the effectiveness and efficiency of our proposed model on network alignment.

Roles are defined as the equivalent classes of isomorphic nodes in the network. They focus on the local connective patterns and describe the structural similarities between nodes, and learning role-based network embeddings can help to recognize identities or functions of entities in real-world networks. This field has been studied over the past decades, however, the existing role-based network embedding methods all concentrate too much on distinguishing node structures and ignore that nodes can belong to different roles even if they have the same local structures. Not only the classical network structure can influence the role of node, but also the emergence of different type of relationship between nodes has impact to it. We believe that roles are influenced by multiple independent factors, and nodes in the same roles should possess both similar local structures and entangled patterns with neighbors hidden in each factor, but most of the existing methods did not clearly point out this challenge. Therefore, we propose a disentangled framework based on graph neural networks to simultaneously model the local structures and interactive relationships in multiple factors to generate role-oriented network embeddings. We design a novel role-aware neighbor choosing mechanism to assign each neighbor a different interactive weight for each latent factor, which can measure its influence on roles. We conduct experiments on synthetic and real-world networks, and the results demonstrate the superiority and effectiveness of our model.

Temporal community detection is helpful to discover and analyze significant groups or clusters hidden in dynamic networks in the real world. A variety of methods, such as modularity optimization, spectral method, and statistical network model, has been developed from diversified perspectives. Recently, network embedding-based technologies have made significant progress, and one can exploit deep learning superiority to network tasks. Although some methods for static networks have shown promising results in boosting community detection by integrating community embedding, they are not suitable for temporal networks and unable to capture their dynamics. Furthermore, the dynamic embedding methods only model network varying without considering community structures. Hence, in this article, we propose a novel unsupervised dynamic community detection model, which is based on network embedding and can effectively discover temporal communities and model dynamic networks. More specifically, we propose the community prior by introducing the Gaussian mixture model (GMM) in the variational autoencoder, which can obtain community information and better model the evolutionary characteristics of community structure and node embedding by utilizing the variant of gated recurrent unit (GRU). Extensive experiments conducted in real-world and artificial networks demonstrate that our proposed model has a better effect on improving the accuracy of dynamic community detection.

Recently, Network Embedding (NE) has become one of the most attractive research topics in machine learning and data mining. NE approaches have achieved promising performance in various graph mining tasks including link prediction and node clustering and classification. A wide variety of NE methods focus on the proximity of networks, they learn community-oriented embedding for each node, where the corresponding representations are similar if two nodes are closer to each other in the network. Meanwhile, there is another type of structural similarity, i.e., role-based similarity, which is completely different from and complementary to the proximity. In order to preserve the role-based structural similarity, the problem of role-oriented NE is raised. However, compared to the community-oriented NE, there are only a few role-oriented embedding approaches proposed recently. Although less explored, considering the importance of roles in analyzing networks and many applications that role-oriented NE can shed light on, it is necessary and timely to provide a comprehensive overview of existing role-oriented NE methods. In this review, we first clarify the differences between community-oriented and role-oriented network embedding. Afterward, we propose a general framework for understanding role-oriented NE and a two-level categorization to better classify existing methods. Then, we select some representative methods according to the proposed categorization and briefly introduce them by discussing their motivation, development, and differences. Moreover, we conduct comprehensive experiments to empirically evaluate these methods on a variety of role-related tasks including node classification and clustering (role discovery), top-k similarity search, and visualization using some widely used synthetic and real-world datasets. Finally, we further discuss the research trend of role-oriented NE from the perspective of applications and point out some potential future directions.

Roles of nodes are defined as classes of equivalent nodes. Nodes that have similar local connective patterns may share the same role. As a complementary concept of community, role can also help to recognize real-world entities. For example, it can denote identity or function in social networks. Role has been studied over the past decades, and learning role-based network representations is crucial to many downstream tasks. The important step for role-based network embedding method is extracting features to measure structural similarity instead of proximity. Although some methods have been developed to capture role features to learn structural similarities between nodes, they all design these features of fixed types, such as the global, local, and higher-order features. These features can only represent a certain type of structure, and it is very difficult to model the complex relationship between different scale features in the field of role-based network embedding. Therefore, we propose a novel role-oriented network embedding framework based on adversarial learning between higher-order and local features (ARHOL) to generate powerful role-based node representations. The higher-order features are discrete so we leverage the Auto-Encoder on them to obtain continuous representations. Then we apply the GIN on its outputs to aggregate local information. Finally, we consider the GIN as the generator and design an adversarial game between local features and GIN outputs to integrate these two aspects of features, which can enhance each other and improve the robustness. The extensive experiments on real-world networks demonstrate the superiority and efficiency of our model, and prove the effectiveness of integrating higher-order and local features.

Role of node is defined on structural similarity or local connective pattern, describing the functions of node in the network. In real-world situation, it can denote person’s identity and status. It has been studied over the past decades, and learning role-based network representations is crucial to many downstream tasks. In this field, the important step for is extracting some measurements to evaluate structural similarity. Although some methods have been developed to capture the role features to learn the structural similarities between nodes, they all design the features of fixed types, such as global, local, and higher-order features. These features can only discover single type of roles, and simply combing them may cause damage to performance. It is very difficult to model the complex relationship between different scale features in the field of role-based network embedding. Therefore, we propose a novel adversarial framework to generate structural node representations via higher-order features and adversarial learning (SHOAL). We leverage the Auto-Encoder on higher-order features and some GNNs on its outputs to aggregate local neighbors. We believe that higher-order and local features can denote roles, and effectively integrating them will help for role discovery. So we consider the GNNs as the generator and design an adversarial game between these features, which can also improve the robustness. The experiments on real-world networks demonstrate the superiority and efficiency of our model, and the results also prove the effectiveness of integrating higher-order and local features.