networkx.algorithms.dag.is_aperiodic¶

is_aperiodic(G)[source]¶

Returns 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

GNetworkX DiGraph: A directed graph

Returns

bool: True if the graph is aperiodic False otherwise

Raises

NetworkXError: If G is not directed

Notes

This uses the method outlined in [1], 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

1: 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.