Algorithm to check if a digraph is complete

Question

Is there a known algorithm for checking whether a graph is a complete digraph?

Ideally, I'd like to find a ready-to-use method from JGraphT Java library.

Alternatively, I've found the following answer regarding completeness check of an undirected graph. Would the following modification work for checking completeness of a directed graph?

check that number of directed edges in the graph is n(n-1)
check that each vertice is directly connected to exactly n-1 distinct vertices

If I don't miss anything and these conditions are sufficient I could implement these checks by myself, but I'd prefer to use existing implementation from the library if possible.

score 2 · Accepted Answer · answered Jul 23 '19 at 06:33

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Can you try this JGraphT method?

GraphTests#isComplete

it says that it checks for digraphs as well.

Test whether a graph is complete. A complete undirected graph is a simple graph in which every pair of distinct vertices is connected by a unique edge. A complete directed graph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction).

answered Jul 23 '19 at 06:33

buræquete

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Thanks, that's exactly what I was looking for! BTW I checked that this method actually checks if the number of edges is equal to n(n-1) assuming the graph is simple. – gregs Jul 23 '19 at 08:33

score 1 · Answer 2 · edited Jul 23 '19 at 10:03

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If your graph doesn't have more than one edge going from and to the same nodes that is the easiest way to do it.

You cannot have a graph that is not complete and has that many (n*(n-1)) edge without duplicated edges.

edited Jul 23 '19 at 10:03

Romil Patel

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answered Jul 23 '19 at 06:33

Tony Barletta

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Algorithm to check if a digraph is complete

2 Answers2