onion_layers

onion_layers(G)

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