Do we always use the word closure under some operation? Usually, I have used the word closure as the set we get after adding element in a set to make that set self content under some operation. For example, closure of $\{1,2,3\}$ under addition is $\mathbb{N}$. Here we are saying closure under addition.
In graph theory, I am not getting if there any operation involved while defining closure of a graph. Is there any operation involved while we are defining closure of a graph ? I want to know the motivation of defining closure of a graph in the way it is defined.