Why one node can be Strongly connected component 
I am learning the strongly connected component. Based on the concept, I do not know why node 7 can be a strongly connected component, because there is not any other node in the component, the node cannot has a path to other. Thank you your help!
 A: Welcome to MSE!
A Strongly Connected Component of a graph $G$ is a subset $C$ of the vertices so that

*

*Every vertex in $C$ has a path in $G$ to every other vertex in $C$ (so $C$ is strongly connected)

*If we add any new vertices to $C$, say $C \cup \{ v_1, \ldots, v_n \}$, then we get something that isn't strongly connected (so $C$ is maximal).

See, for instance, the wikipedia page for more information.
First notice every $\{v\}$ is automatically strongly connected -- there are no "other" vertices in $C$ to need a path to! Equivalently, if you prefer, every vertex has a path to itself (of length $0$).
So to ask why $\{ 7 \}$ is a strongly connected component, we need to know that $\{ 7 \}$ is maximal with this property. So no matter what vertices we add, we'll get something that isn't strongly connected. Do you see why this might be the case? I'll leave a hint under the fold.

 Notice $7$ only has a path graphs in the right hand side of the graph, but nothing on the right hand side can get to $7$. Moreover, vertices on the left hand side of the graph can get to $7$, but $7$ can't get back to them. So no matter which vertices we add, they'll either be unable to reach $7$, or $7$ will be unable to reach them.

As an aside, it's important to allow these "degenerate" cases, where $\{ 7 \}$ is strongly connected. We want to know that every vertex is in some strongly connected component, and we need to allow $\{ v \}$ as an option to make that true.

I hope this helps ^_^
