For each even number n greater than 2, there exists a 3-regular graph with n nodes. I am having a hard time of understanding a proof in the book, "Introduction to the Theory of Computation, Third Edition (international)",  In page 21.
PROOF
Let $n$ be an even number greater than 2. Construct graph $G = (V,E)$
with n nodes as follows. The set of nodes of G is $V = \{0, 1, . . . , n − 1\}$, and the set of edges of G is the set
  E =   { {i, i + 1} | for 0  i  n − 2}
        U { {n − 1, 0} }
        U {{i, i + n/2} | for 0  i  n/2 − 1}.

picture the nodes of this graph written consecutively around the circumference of a circle. In that case, the edges described in the top line of E go between adjacent pairs around the circle. The edges described in the bottom line of E go between nodes on opposite sides of the circle. This mental picture clearly shows that every node in G has degree 3.
I apologize in advance if this is a too simple of a question. English is not my first language and I am having a hard time of following the author's idea. Please help.
My questions are:

*

*What does it means "the edges described in the top line of E go between adjacent pairs around the circle?"

*In the set above, What part describes the top line of E?

*It seems to me that there are 3 sets describing the E. IF we use top part and the bottom part, What does the rest part do?

Thank you so much in advance.


\begin{eqnarray*}
E =   \{ (i, i + 1) | \text{for } i= 0 \cdots  n − 2 \} \cup \{ (n − 1, 0) \} \\
        \cup \color{red}{ \{(i, i + n/2) | \text{for }   i=0 \cdots  n/2 − 1 \} }.
\end{eqnarray*}
