  Network embedding which encodes all vertices in a network as a set of
numerical vectors in accordance with it's local and global structures, has
drawn widespread attention. Network embedding not only learns significant
features of a network, such as the clustering and linking prediction but also
learns the latent vector representation of the nodes which provides theoretical
support for a variety of applications, such as visualization, node
classification, and recommendation. As the latest progress of the research,
several algorithms based on random walks have been devised. Although their high
scores for learning efficiency and accuracy have drawn much attention, there is
still a lack of theoretical explanation, and the transparency of the algorithms
has been doubted. Here, we propose an approach based on the open-flow network
model to reveal the underlying flow structure and its hidden metric space of
different random walk strategies on networks. We show that the essence of
embedding based on random walks is the latent metric structure defined on the
open-flow network. This not only deepens our understanding of random walk based
embedding algorithms but also helps in finding new potential applications in
embedding.
