  Real-world networks usually have community structure, that is, nodes are
grouped into densely connected communities. Community detection is one of the
most popular and best-studied research topics in network science and has
attracted attention in many different fields, including computer science,
statistics, social sciences, among others. Numerous approaches for community
detection have been proposed in literature, from ad-hoc algorithms to
systematic model-based approaches. The large number of available methods leads
to a fundamental question: whether a certain method can provide consistent
estimates of community labels. The stochastic blockmodel (SBM) and its variants
provide a convenient framework for the study of such problems. This article is
a survey on the recent theoretical advances of community detection. The authors
review a number of community detection methods and their theoretical
properties, including graph cut methods, profile likelihoods, the
pseudo-likelihood method, the variational method, belief propagation, spectral
clustering, and semidefinite relaxations of the SBM. The authors also briefly
discuss other research topics in community detection such as robust community
detection, community detection with nodal covariates and model selection, as
well as suggest a few possible directions for future research.
