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I know this might be similar to this question, but I would like to know what the maximum number of edges in a digraph would be if parallel edges (aka multi-edges) are not allowed. I know that the maximum number of edges, given V vertices, would be V * (V - 1).

Community
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yiwei
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2 Answers2

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You say:

"I know that the maximum number of edges, given V vertices, would be V * (V - 1)."

But this is not true of a graph that is not directed. Given n verticies, it's actually nC2 = n(n-1)/2. I think, but I'm not sure, that this what you were looking for.

If the graph is directed (that is Va -> Vb is not the same line as Vb -> Va), then it raises to the n * (n-1) you quote.

If the graph allow you to have edges from a node to itself, the total number is n^2.

J. A. Streich
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If parallel edges are not allowed in a diagraph (i.e. if edge a -> b exists, then b - > a is not allowed), the maximum number of edges would be simple VC2 or (V*(V-1))/2

Shubham Mittal
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