  The paper considers the Popularity Adjusted Block model (PABM) introduced by
Sengupta and Chen (2018). We argue that the main appeal of the PABM is the
flexibility of the spectral properties of the graph which makes the PABM an
attractive choice for modeling networks that appear in biological sciences. We
expand the theory of PABM to the case of an arbitrary number of communities
which possibly grows with a number of nodes in the network and is not assumed
to be known. We produce the estimators of the probability matrix and the
community structure and provide non-asymptotic upper bounds for the estimation
and the clustering errors. We use the Sparse Subspace Clustering (SSC) approach
to partition the network into communities, the approach that, to the best of
our knowledge, has not been used for clustering network data. The theory is
supplemented by a simulation study. In addition, we show advantages of the PABM
for modeling a butterfly similarity network and a human brain functional
network.
