RiWalk: Fast Structural Node Embedding via Role Identification Nodes performing different functions in a network have different roles, and these roles can be gleaned from the structure of the network. Learning latent representations for the roles of nodes helps to understand the network and to transfer knowledge across networks. However, most existing structural embedding approaches suffer from high computation and space cost or rely on heuristic feature engineering. Here we propose RiWalk, a flexible paradigm for learning structural node representations as it decouples the structural embedding problem into a role identification procedure and a network embedding procedure. Through role identification, rooted kernels with structural dependencies kept are built to better integrate network embedding methods. To demonstrate the effectiveness of RiWalk, we develop two different role identification methods named RiWalkSP and RiWalkWL respectively and employ random walk based network embedding methods. Experiments on withinnetwork classification tasks show that our proposed algorithms achieve comparable performance with other baselines while being an order of magnitude more efficient. Besides, we also conduct acrossnetwork role classification tasks. The results show potential of structural embeddings in transfer learning. RiWalk is also scalable, making it capable of capturing structural roles in massive networks.

Network2Vec: Learning Node Representation Based on Space Mapping in Networks Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn a fixedlength vector for each node in an embedding space, where the node properties in the original graph are preserved. Existing methods mainly focus on learning embedding vectors to preserve nodes proximity, i.e., nodes next to each other in the graph space should also be closed in the embedding space, but do not enforce algebraic statistical properties to be shared between the embedding space and graph space. In this work, we propose a lightweight model, entitled Network2Vec, to learn network embedding on the base of semantic distance mapping between the graph space and embedding space. The model builds a bridge between the two spaces leveraging the property of group homomorphism. Experiments on different learning tasks, including node classification, link prediction, and community visualization, demonstrate the effectiveness and efficiency of the new embedding method, which improves the stateoftheart model by 19% in node classification and 7% in link prediction tasks at most. In addition, our method is significantly faster, consuming only a fraction of the time used by some famous methods.