An improved spectral clustering method for community detection under the degree-corrected stochastic blockmodel

To solve the community detection problem, substantial approaches, such as Snijders and Nowicki (1997); Nowicki and Snijders (2001); Daudin et al. (2008); Bickel and Chen (2009); Rohe et al. (2011); Amini et al. (2013), are designed based on the standard framework, the stochastic block model (SBM) (Holland et al. (1983)), since it is mathematically simple and relatively easy to analyze (Bickel and Chen (2009)). However, the assumptions of SBM are too restrictive to implement in real networks. It is assumed that the distribution of degrees within the community is Poisson, that is, the nodes within each community have the same expected degrees. Unfortunately, in many natural networks, the degrees follow approximately a power-law distribution (Kolaczyk (2009); Goldenberg et al. (2010); Jin(2015)). The corrected-degree stochastic block model (DCSBM) (Karrer and Newman (2011)) is developed based on the power-law distribution which allows the degree of nodes varies among different communities.