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.

Deprecated since version 3.3: k_shell will not accept MultiGraph objects in version 3.5.

GNetworkX graph

A graph or directed graph.

kint, optional

The order of the shell. If not specified return the outer shell.

core_numberdictionary, optional

Precomputed core numbers for the graph G.

GNetworkX graph

The k-shell subgraph


The k-shell is not implemented for multigraphs or graphs with self loops.


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

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.



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


>>> degrees = [0, 1, 2, 2, 2, 2, 3]
>>> H = nx.havel_hakimi_graph(degrees)
>>> H.degree
DegreeView({0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 3, 6: 0})
>>> nx.k_shell(H, k=1).nodes
NodeView((0, 4))