# WeaklyConnectedGraphQ evaluates to False. Is this the expected result?

Take the simple graph {1->2, 2->3, 3->1}:

TreePlot[{1->2,2->3,3->1}]

I would expect that WeaklyConnectedGrapghQ[{1->2,2->3,3->1}] evaluates to True, but in fact I get False, so I was wondering if maybe my concept of connectet graph is wrong. Is this graph (weakly) connected or Mathematica is right and the correct output is False?.

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– Michael E2
Oct 17 ’15 at 12:49

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In general, all functions ending in Q will return either True or False, but nothing else.

You can think of WeaklyConnectedGraphQ as testing that it’s argument is a graph and that it is weakly connected.

{1->2,2->3,3->1} is not a graph, it is a list of rules. Thus WeaklyConnectedGraphQ returns False.

g = Graph[{1->2,2->3,3->1}] creates a graph from the rule list. WeaklyConnectedGraphQ[g] returns True.

This is it, thank you.
– AccidentalFourierTransform
Oct 17 ’15 at 13:23