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Complex networks represented as node adjacency matrices constrains theapplication of machine learning and parallel algorithms. To address thislimitation, network embedding (i.e., graph representation) has been intensivelystudied to learn a fixed-length vector for each node in an embedding space,where the node properties in the original graph are preserved. Existing methodsmainly 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 theembedding space, but do not enforce algebraic statistical properties to beshared between the embedding space and graph space. In this work, we propose alightweight model, entitled Network2Vec, to learn network embedding on the baseof semantic distance mapping between the graph space and embedding space. Themodel builds a bridge between the two spaces leveraging the property of grouphomomorphism. Experiments on different learning tasks, including nodeclassification, link prediction, and community visualization, demonstrate theeffectiveness and efficiency of the new embedding method, which improves thestate-of-the-art model by 19% in node classification and 7% in link predictiontasks at most. In addition, our method is significantly faster, consuming onlya fraction of the time used by some famous methods.

Network2Vec Learning Node Representation Based on Space Mapping in Networks