networkx.algorithms.core.core_number

core_number(G)[source]

Returns the core number for each vertex.

A k-core is a maximal subgraph that contains nodes of degree k or more.

The core number of a node is the largest value k of a k-core containing that node.

Parameters
GNetworkX graph

A graph or directed graph

Returns
core_numberdictionary

A dictionary keyed by node to the core number.

Raises
NetworkXError

The k-core is not implemented for graphs with self loops or parallel edges.

Notes

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.

References

1

An O(m) Algorithm for Cores Decomposition of Networks Vladimir Batagelj and Matjaz Zaversnik, 2003. https://arxiv.org/abs/cs.DS/0310049