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Weakly Connected Directed Graphs | Digraph Theory
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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.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
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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.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
********************************************************************
+WRATH OF MATH+
Follow Wrath of Math on...
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