Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

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:
  • 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]
    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].