Line graph of $\Bbb K_{3,3}$ is self complementary 
How do I show the line graph of $\Bbb K_{3,3}$ is self-complementary?

I know that a graph is self complementary if it is isomorphic to its complement. I can prove it using drawing the line graph of $\Bbb K_{3,3}$ and then finding complement of it. Is there any easier way of doing it?
Please let me know.

I don't know if it's easier, but here is one way to do it.
Let $K_{3,3}$ have vertices $u_0,u_1,u_2$ on one side and $v_0,v_1,v_2$ on the other side. Identify the edge $u_iv_j$ with the ordered pair $(i,j)\in\mathbb Z_3\times\mathbb Z_3$, where $(\mathbb Z_3,+)$ is the cyclic group of order $3$. Then the graph $G=L(K_{3,3})$ has vertex set $\mathbb Z_3\times\mathbb Z_3$, and two distinct vertices $(i,j)$ and $(i',j')$ are adjacent iff $i=i'$ or $j=j'$. The mapping $(i,j)\mapsto(i+j,i-j)$ is an isomorphism from the graph $G$ to its complement.
