power¶

power(G, k)[source]¶

Returns the specified power of a graph.

The $k$ -th power of a simple graph $G = (V, E)$ is the graph $G^k$ whose vertex set is $V$ , two distinct vertices $u,v$ are adjacent in $G^k$ if and only if the shortest path distance between $u$ and $v$ in $G$ is at most $k$ .

Parameters:	G (graph) – A NetworkX simple graph object. k (positive integer) – The power to which to raise the graph $G$ .
Returns:	$G$ to the $k$ -th power.
Return type:	NetworkX simple graph
Raises:	exc: $ValueError$ – If the exponent $k$ is not positive. `NetworkXError` – If G is not a simple graph.

Examples

>>> G = nx.path_graph(4)
>>> nx.power(G,2).edges()
[(0, 1), (0, 2), (1, 2), (1, 3), (2, 3)]
>>> nx.power(G,3).edges()
[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]

A complete graph of order n is returned if k is greater than equal to n/2 for a cycle graph of even order n, and if k is greater than equal to (n-1)/2 for a cycle graph of odd order.

>>> G = nx.cycle_graph(5)
>>> nx.power(G,2).edges() == nx.complete_graph(5).edges()
True
>>> G = nx.cycle_graph(8)
>>> nx.power(G,4).edges() == nx.complete_graph(8).edges()
True

References

[1]	Bondy, U. S. R. Murty, Graph Theory. Springer, 2008.

Notes

Exercise 3.1.6 of Graph Theory by J. A. Bondy and U. S. R. Murty [1].