is_aperiodic¶

is_aperiodic(G)[source]¶

Return True if G is aperiodic.

A directed graph is aperiodic if there is no integer k > 1 that divides the length of every cycle in the graph.

Parameters:

G : NetworkX DiGraph

Graph

Returns:

aperiodic : boolean

True if the graph is aperiodic False otherwise

Raises:

NetworkXError

If G is not directed

Notes

This uses the method outlined in [R236], which runs in O(m) time given m edges in G. Note that a graph is not aperiodic if it is acyclic as every integer trivial divides length 0 cycles.

References

[R236]

(1, 2) Jarvis, J. P.; Shier, D. R. (1996), Graph-theoretic analysis of finite Markov chains, in Shier, D. R.; Wallenius, K. T., Applied Mathematical Modeling: A Multidisciplinary Approach, CRC Press.