Weakly Connected Directed Graphs | Digraph Theory

What is a connected digraph? When we start considering directed graphs, we have to rethink our definition of connected. We say that an undirected graph is connected if there exists a path connecting every pair of vertices. However, in a directed graph, we need to be more specific since it is possible there exists a u-v path but no v-u path.
Recall that the underlying graph of a directed graph is obtained by removing the direction from the edges of the directed graph. If the underlying graph of a digraph D is connected, then we say the digraph D is weakly connected. Thus, for this particular measure of connectivity, we defer back to undirected graphs and the original definition of connected. However, there is a stronger definition for a stronger type of connectivity in digraphs. What do you think it is?
If the underlying graph of a directed graph is disconnected, we also call the directed graph disconnected.
Lesson on underlying graphs: • Underlying Graphs of D...
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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[@PunmasterSTP]

Weakly connected, but wickedly cool!

[@sebastianamaruescalantecco7916]

Thank you, very well explained!

[@WrathofMath]

My pleasure, glad it helped and thanks for watching!

[@ibhruti]

Short sweet simple, great video👍

[@WrathofMath]

Thanks a lot! If you're looking for more graph theory, check out my playlist! czcams.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
And let me know if you have any questions!

[@muhammadsaimiqbal1551]

please make a video on pigeon hole principle

[@CHAOSTECH]

Where can I find the video about strongly connectedness?

[@WrathofMath]

Thanks for watching and right here! :) czcams.com/video/2fzSEMNEXhU/video.html

[@hotaekhan3785]

Thanks for excellent video, sir. But I have a question. You said let be D a directed graph. then D is weakly connected if the underlying graph of D is connect. But Is D neccessarily a weakly connected graph? Is D can't be a strongly connected graph? I don't know what I'm missing..

[@WrathofMath]

Thanks for watching and good question, Hotaek! If the underlying graph of D is connected, then indeed D is necessarily weakly connected. However this does NOT forbid D from being strongly connected. Strongly connected graphs are a subset of weakly connected graphs! Hope that clears it up!
EDIT: Fixed mistake

[@hotaekhan3785]

@@WrathofMath Thanks for kind reply! But If so, are strongly connected graphs a subset of weakly connected graphs? Because if graph D is a strongly connected graph, graph D is weakly connected graph.

[@WrathofMath]

Yes, you’re exactly right! My mistake! I should be more careful answering comments early in the morning haha! I am going to edit my previous comment to make it correct.

[@hotaekhan3785]

@@WrathofMath Oh now I understood. Thanks!!

[@manikkudyar1159]

Excellent sir

[@WrathofMath]

Thanks a lot, Manik!

[@ramumaha2779]

awesome sir

[@WrathofMath]

Thank you!

[@omaimad4120]

thanks !

[@WrathofMath]

Glad to help!