Suppose you have a directed graph. Vertices a and b are part of the graph. There is an arrow pointing from a to b and an arrow pointing from b to a. Does this make the directed graph cyclic?

  • $\begingroup$ I would like to note that, as with most things in math (and by extension computer science) the statement of the definition that is in use in the discussion should be used to answer this. But it is also useful to question the generally understood notion of cyclic graphs. $\endgroup$
    – Odo Frodo
    Oct 21, 2017 at 17:22

1 Answer 1


Yes the graph is cyclic. It does not matter how many vertices are there. If a cycle can be formed then the graph is cyclic. You can even form a cyclic graph with one node. This cycle would be called a self loop.


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