Today I read a paper titled “Generalized Cores”
The abstract is:
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.