Is it guaranteed that in a directed graph with multiple vertices, where vertices A and B are connected to each other, and the connection involves intermediate vertices (C, D, E), ensuring mutual reachability between A and B, the intermediate vertices (C, D, E) will always be part of the same strongly connected component (SCC) as A and B? If not kindly share the example of the same .
Example If vertice A is directly connected with B . And B is connected to A via some vertices C,D and E. Will this guarantee A,B,C,D,E will always be part of one SCC {A,B,C,D,E} in any setup?
I am not able to come with a graph where the above assumption is not valid .
The definition of a strongly connected component is that each vertex in it is reachable from each other vertex. If vertex B can reach A by passing through vertices X, and vertex A can also reach vertex B, then there is a cycle. Following this cycle allows each vertex to reach each other vertex, and thus they are part of the same SCC.