  This paper focuses on two fundamental tasks of graph analysis: community
detection and node representation learning, which capture the global and local
structures of graphs, respectively. In the current literature, these two tasks
are usually independently studied while they are actually highly correlated. We
propose a probabilistic generative model called vGraph to learn community
membership and node representation collaboratively. Specifically, we assume
that each node can be represented as a mixture of communities, and each
community is defined as a multinomial distribution over nodes. Both the mixing
coefficients and the community distribution are parameterized by the
low-dimensional representations of the nodes and communities. We designed an
effective variational inference algorithm which regularizes the community
membership of neighboring nodes to be similar in the latent space. Experimental
results on multiple real-world graphs show that vGraph is very effective in
both community detection and node representation learning, outperforming many
competitive baselines in both tasks. We show that the framework of vGraph is
quite flexible and can be easily extended to detect hierarchical communities.
