  Spectral clustering is a popular method for community detection in network
graphs: starting from a matrix representation of the graph, the nodes are
clustered on a low dimensional projection obtained from a truncated spectral
decomposition of the matrix. Estimating correctly the number of communities and
the dimension of the reduced latent space is critical for good performance of
spectral clustering algorithms. Furthermore, many real-world graphs, such as
enterprise computer networks studied in cyber-security applications, often
display heterogeneous within-community degree distributions. Such heterogeneous
degree distributions are usually not well captured by standard spectral
clustering algorithms. In this article, a novel spectral clustering algorithm
is proposed for community detection under the degree-corrected stochastic
blockmodel. The proposed method is based on a transformation of the spectral
embedding to spherical coordinates, and a novel modelling assumption in the
transformed space. The method allows for simultaneous and automated selection
of the number of communities and the latent dimension for spectral embeddings
of graphs with uneven node degrees. Results show improved performance over
competing methods in representing computer networks.
