Test cases
("." is an empty node)

Case #1

A --> . <-- B
move A, resulting in:
. --> A <-- B
or move B, resulting in:
A --> B <-- .

Case #2

A --> B --> .
move both A and B:
. --> A --> B

Case #3

A --> . <-- B <-- C
Move B and C, since that is one more object moved than just moving A:
A --> B <-- C <-- .

Case #4

A <--> B
Switch the positions of A and B:
B <--> A

Case #5

B --> C
^     |
|     |
|     v
A <-- D <-- E
Rotate each member of the cycle:
A --> B
^     |
|     |
|     v
D <-- C <-- E

Case #6

B --> C
^     |
|     |
|     v
A <-- D <-- E <-- F
      |           ^
      |           |
      v           |
      I --> H --> G
Only one cycle can be rotated; choose the longer one
B --> C
^     |
|     |
|     v
A <-- E <-- F <-- G
      |           ^
      |           |
      v           |
      D --> I --> H