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Note

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

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networkx.generators.community.connected_caveman_graph

connected_caveman_graph(l, k)[source]

Returns a connected caveman graph of l cliques of size k.

The connected caveman graph is formed by creating n cliques of size k, then a single edge in each clique is rewired to a node in an adjacent clique.

Parameters

  • l (int) – number of cliques

  • k (int) – size of cliques (k at least 2 or NetworkXError is raised)

Returns

G – connected caveman graph

Return type

NetworkX Graph

Raises

NetworkXError – If the size of cliques k is smaller than 2.

Notes

This returns an undirected graph, it can be converted to a directed graph using nx.to_directed(), or a multigraph using nx.MultiGraph(nx.caveman_graph(l, k)). Only the undirected version is described in 1 and it is unclear which of the directed generalizations is most useful.

Examples

>>> G = nx.connected_caveman_graph(3, 3)

References

1

Watts, D. J. ‘Networks, Dynamics, and the Small-World Phenomenon.’ Amer. J. Soc. 105, 493-527, 1999.