  Most of the existing graph embedding methods focus on nodes, which aim to output a vector representation for each node in the graph such that two nodes being "close" on the graph are close too in the low-dimensional space. Despite the success of embedding individual nodes for graph analytics, we notice that an important concept of embedding communities (i.e., groups of nodes) is missing. Embedding communities is useful, not only for supporting various community-level applications, but also to help preserve community structure in graph embedding. In fact, we see community embedding as providing a higher-order proximity to define the node closeness, whereas most of the popular graph embedding methods focus on first-order and/or second-order proximities. To learn the community embedding, we hinge upon the insight that community embedding and node embedding reinforce with each other. As a result, we propose ComEmbed, the first community embedding method, which jointly optimizes the community embedding and node embedding together. We evaluate ComEmbed on real-world data sets. We show it outperforms the state-of-the-art baselines in both tasks of node classification and community prediction. 
From Node Embedding To Community Embedding