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Mike Sanz
Mike Sanz
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A digraph is a directed graph.

A directed cycle or simple directed circuit is a directed circuit in which the only repeated vertices are the first and last vertices.

A digraph is primitive if its adjacency matrix is primitive.

A square non-negative matrix $A$ is said to be primitive if there exists a positive integer $k$ such that $A^k >0$ (all entries of $A^k$ are positive).

I need only the existence of a path with the structure $i_0 i_1...i_k i_0$ (sequence of distinc edges) with $k\geq 1$.

A digraph is a directed graph.

A directed cycle or simple directed circuit is a directed circuit in which the only repeated vertices are the first and last vertices.

A digraph is primitive if its adjacency matrix is primitive.

A square non-negative matrix $A$ is said to be primitive if there exists a positive integer $k$ such that $A^k >0$ (all entries of $A^k$ are positive).

A digraph is a directed graph.

A directed cycle or simple directed circuit is a directed circuit in which the only repeated vertices are the first and last vertices.

A digraph is primitive if its adjacency matrix is primitive.

A square non-negative matrix $A$ is said to be primitive if there exists a positive integer $k$ such that $A^k >0$ (all entries of $A^k$ are positive).

I need only the existence of a path with the structure $i_0 i_1...i_k i_0$ (sequence of distinc edges) with $k\geq 1$.

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Mike Sanz
Mike Sanz
  • 121
  • 6

Does every primitive digraph have a directed cycle?

A digraph is a directed graph.

A directed cycle or simple directed circuit is a directed circuit in which the only repeated vertices are the first and last vertices.

A digraph is primitive if its adjacency matrix is primitive.

A square non-negative matrix $A$ is said to be primitive if there exists a positive integer $k$ such that $A^k >0$ (all entries of $A^k$ are positive).