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.
Examples
A graph consisting of one cycle, the length of which is 2. Therefore
k = 2
divides the length of every cycle in the graph and thus the graph is not aperiodic:>>> DG = nx.DiGraph([(1, 2), (2, 1)]) >>> nx.is_aperiodic(DG) False
A graph consisting of two cycles: one of length 2 and the other of length 3. The cycle lengths are coprime, so there is no single value of k where
k > 1
that divides each cycle length and therefore the graph is aperiodic:>>> DG = nx.DiGraph([(1, 2), (2, 3), (3, 1), (1, 4), (4, 1)]) >>> nx.is_aperiodic(DG) True
A graph consisting of two cycles: one of length 2 and the other of length 4. The lengths of the cycles share a common factor
k = 2
, and therefore the graph is not aperiodic:>>> DG = nx.DiGraph([(1, 2), (2, 1), (3, 4), (4, 5), (5, 6), (6, 3)]) >>> nx.is_aperiodic(DG) False
An acyclic graph, therefore the graph is not aperiodic:
>>> DG = nx.DiGraph([(1, 2), (2, 3)]) >>> nx.is_aperiodic(DG) False