core_number¶

core_number(G)[source]¶

Return 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:

G : NetworkX graph

A graph or directed graph

Returns:

core_number : dictionary

A dictionary keyed by node to the core number.

Raises:

NetworkXError

The k-core is not defined 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

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