We propose a robust, scalable, integrated methodology for community detection
and community comparison in graphs. In our procedure, we first embed a graph
into an appropriate Euclidean space to obtain a low-dimensional representation,
and then cluster the vertices into communities. We next employ nonparametric
graph inference techniques to identify structural similarity among these
communities. These two steps are then applied recursively on the communities,
allowing us to detect more fine-grained structure. We describe a hierarchical
stochastic blockmodel---namely, a stochastic blockmodel with a natural
hierarchical structure---and establish conditions under which our algorithm
yields consistent estimates of model parameters and motifs, which we define to
be stochastically similar groups of subgraphs. Finally, we demonstrate the
effectiveness of our algorithm in both simulated and real data. Specifically,
we address the problem of locating similar subcommunities in a partially
reconstructed Drosophila connectome and in the social network Friendster.

该论文提出了一种强大、可扩展、综合的图中社区检测和比较方法，首先将图嵌入到一个适当的欧几里得空间中以获得低维表示，然后将顶点聚类成社区，并应用非参数图推理技术识别这些社区之间的结构相似性，然后可以递归地应用这两个步骤到社区上，以检测更细粒度的结构。最后，在模拟和真实数据上证明了该算法的有效性。