# networkx.algorithms.core.k_shell¶

k_shell(G, k=None, core_number=None)[source]

Returns the k-shell of G.

The k-shell is the subgraph induced by nodes with core number k. That is, nodes in the k-core that are not in the (k+1)-core.

Parameters
• G (NetworkX graph) – A graph or directed graph.

• k (int, optional) – The order of the shell. If not specified return the outer shell.

• core_number (dictionary, optional) – Precomputed core numbers for the graph G.

Returns

G – The k-shell subgraph

Return type

NetworkX graph

Raises

NetworkXError – The k-shell is not implemented for graphs with self loops or parallel edges.

Notes

This is similar to k_corona but in that case only neighbors in the k-core are considered.

Not implemented for graphs with parallel edges or self loops.

For directed graphs the node degree is defined to be the in-degree + out-degree.

Graph, node, and edge attributes are copied to the subgraph.

References

1

A model of Internet topology using k-shell decomposition Shai Carmi, Shlomo Havlin, Scott Kirkpatrick, Yuval Shavitt, and Eran Shir, PNAS July 3, 2007 vol. 104 no. 27 11150-11154 http://www.pnas.org/content/104/27/11150.full