# Is a single node graph a strongly connected component?

Can a single node graph be considered a (strongly) connected component?

I'm confused because I was reading about cut vertex which by definition is a vertex that if eliminated increases the number of connected components.

So if we were to remove vertex number 2, we would get 2 connected components?

Thanks!

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A graph is connected if every pair of vertices in the graph can be connected by a path. By definition a single vertex is connected to itself by the trivial path. Hence, it is connected. If the graph is directed the same argument applies.