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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 – True if the graph is aperiodic False otherwise
Return type:boolean
Raises:NetworkXError – If G is not directed


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.


[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.