  Local network community detection aims to find a single community in a large
network, while inspecting only a small part of that network around a given seed
node. This is much cheaper than finding all communities in a network. Most
methods for local community detection are formulated as ad-hoc optimization
problems. In this work, we instead start from a generative model for networks
with community structure. By assuming that the network is uniform, we can
approximate the structure of unobserved parts of the network to obtain a method
for local community detection. We apply this local approximation technique to
two variants of the stochastic block model. To our knowledge, this results in
the first local community detection methods based on probabilistic models.
Interestingly, in the limit, one of the proposed approximations corresponds to
conductance, a popular metric in this field. Experiments on real and synthetic
datasets show comparable or improved results compared to state-of-the-art local
community detection algorithms.
