WeaklyConnectedGraphQ
WeaklyConnectedGraphQ[g] yields True if the graph g is weakly connected, and False otherwise.
Examples
Test if a graph is weakly connected:
g = Graph[{1 -> 2, 2 -> 3}];
WeaklyConnectedGraphQ[g]
(* True *)Disconnected graph:
WeaklyConnectedGraphQ[Graph[{1 -> 2, 3 -> 4}]]
(* False *)Please visit the official Wolfram Language Reference for more details.