Generalized Cores
  Cores are, besides connectivity components, one among few concepts that provides us with efficient decompositions of large graphs and networks.   In the paper a generalization of the notion of core of a graph based on vertex property function is presented. It is shown that for the local monotone vertex property functions the corresponding cores can be determined in $O(m \max (\Delta, \log n))$ time. 
V. Batagelj and M. Zaver\v{s}nik