Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

networkx.algorithms.core.onion_layers

onion_layers(G)[source]

Returns the layer of each vertex in an onion decomposition of the graph.

The onion decomposition refines the k-core decomposition by providing information on the internal organization of each k-shell. It is usually used alongside the core numbers.

Parameters
GNetworkX graph

A simple graph without self loops or parallel edges

Returns
od_layersdictionary

A dictionary keyed by vertex to the onion layer. The layers are contiguous integers starting at 1.

Raises
NetworkXError

The onion decomposition is not implemented for graphs with self loops or parallel edges or for directed graphs.

See also

core_number

Notes

Not implemented for graphs with parallel edges or self loops.

Not implemented for directed graphs.

References

1

Multi-scale structure and topological anomaly detection via a new network statistic: The onion decomposition L. Hébert-Dufresne, J. A. Grochow, and A. Allard Scientific Reports 6, 31708 (2016) http://doi.org/10.1038/srep31708

2

Percolation and the effective structure of complex networks A. Allard and L. Hébert-Dufresne Physical Review X 9, 011023 (2019) http://doi.org/10.1103/PhysRevX.9.011023