networkx.generators.community.windmill_graph

windmill_graph(n, k)[source]

Generate a windmill graph. A windmill graph is a graph of n cliques each of size k that are all joined at one node. It can be thought of as taking a disjoint union of n cliques of size k, selecting one point from each, and contracting all of the selected points. Alternatively, one could generate n cliques of size k-1 and one node that is connected to all other nodes in the graph.

Parameters

  • n (int) – Number of cliques

  • k (int) – Size of cliques

Returns

G – windmill graph with n cliques of size k

Return type

NetworkX Graph

Raises

NetworkXError – If the number of cliques is less than two If the size of the cliques are less than two

Examples

>>> G = nx.windmill_graph(4, 5)

Notes

The node labeled 0 will be the node connected to all other nodes. Note that windmill graphs are usually denoted Wd(k,n), so the parameters are in the opposite order as the parameters of this method.