  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 fixed-length 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
state-of-the-art 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.
