Spider Puzzle (Front Door)

Hint 1 of 6:

A pattern is the key to solving this puzzle.

Hint 2 of 6:

You should try filling in the gaps that are created when a spider moves
from one point to another.

Hint 3 of 6:

Or to be specific, make sure that a spider ends up on the same point that
the last spider _started_ on.

Hint 4 of 6:

In other words, take an example where point A is connected to points B and C.

Hint 5 of 6:

Then put a spider on point A and move it to B.