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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 [R233], 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
[R233] (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.