Find the k-cores of a graph.

The k-core is found by recursively pruning nodes with degrees less than k.

See the following references for details:

An O(m) Algorithm for Cores Decomposition of Networks Vladimir Batagelj and Matjaz Zaversnik, 2003.

Generalized Cores Vladimir Batagelj and Matjaz Zaversnik, 2002.

For directed graphs a more general notion is that of D-cores which looks at (k, l) restrictions on (in, out) degree. The (k, k) D-core is the k-core.

D-cores: Measuring Collaboration of Directed Graphs Based on Degeneracy Christos Giatsidis, Dimitrios M. Thilikos, Michalis Vazirgiannis, ICDM 2011.

core_number(G) Return the core number for each vertex.
k_core(G[, k, core_number]) Return the k-core of G.
k_shell(G[, k, core_number]) Return the k-shell of G.
k_crust(G[, k, core_number]) Return the k-crust of G.
k_corona(G, k[, core_number]) Return the k-corona of G.