{
  "id": "enwiki-001319831780",
  "slug": "aperiodic-graph",
  "title": "Aperiodic graph",
  "qid": "",
  "lead": "with period three. In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph. Equivalently, a graph is aperiodic if the greatest common divisor of the lengths of its cycles is one; this greatest common divisor for a graph G is called the period of G.",
  "body": "with period three.]] In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph. Equivalently, a graph is aperiodic if the greatest common divisor of the lengths of its cycles is one; this greatest common divisor for a graph G is called the period of G. For each e in G that connects a vertex on level i of the depth-first search tree to a vertex on level j, let k e = j − i − 1. Compute the greatest common divisor of the set of numbers k e . The graph is aperiodic if and only if the period computed in this fashion is 1. If G is not strongly connected, we may perform a similar computation in each strongly connected component of G, ignoring the edges that pass from one strongly connected component to another. Jarvis and Shier describe a very similar algorithm using breadth first search in place of depth-first search; the advantage of depth-first search is that the strong connectivity analysis can be incorporated into the same search. ==References== . .",
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    "title": "Aperiodic graph",
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        "family": "Anticloud FZ LLE",
        "literal": "Anticloud FZ LLE"
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    ],
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    "publisher": "Anticloud FZ LLE",
    "publisher-place": "Dubai, United Arab Emirates",
    "URL": "https://encyclopegia.org/a/aperiodic-graph",
    "issued": {
      "date-parts": [
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          2026,
          11,
          15
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    "DOI": "eo1:enwiki-001319831780",
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