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power

power(G, k)

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:

• 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].