The adjacency matrix below defines a directed graph 𝐺 with vertices 𝐴,𝐵,𝐶,𝐷,𝐸,𝐹,𝐺,𝐻Write down the strong connected components as sets of vertices separated by commas and enclosed by braces.Hint: we recommend drawing the graph on your scrap paper.0 0 1 0 0 1 0 00 0 0 0 1 1 0 00 0 1 1 0 0 0 00 0 0 0 0 0 1 01 0 0 0 0 0 1 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 1 0 0 0 1 1 0Your Answer:
Question
The adjacency matrix below defines a directed graph 𝐺 with vertices 𝐴,𝐵,𝐶,𝐷,𝐸,𝐹,𝐺,𝐻Write down the strong connected components as sets of vertices separated by commas and enclosed by braces.Hint: we recommend drawing the graph on your scrap paper.0 0 1 0 0 1 0 00 0 0 0 1 1 0 00 0 1 1 0 0 0 00 0 0 0 0 0 1 01 0 0 0 0 0 1 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 1 0 0 0 1 1 0Your Answer:
Solution
The adjacency matrix represents the following directed graph:
- A is connected to C and F.
- B is connected to E and F.
- C is connected to C and D.
- D is connected to G.
- E is connected to A and G.
- F is connected to B.
- G is connected to C.
- H is connected to B, F, and G.
From this, we can identify the strongly connected components (sets of vertices where every vertex is reachable from every other vertex in the set) as:
- {C}
- {B, F}
- {A, E, G, D}
So, the strongly connected components of the graph are {C}, {B, F}, and {A, E, G, D}.
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