Oh Patterns... There's More Than Meets the Eye!!

I guess everybody nowadays is familiar with the unlock screens of every Android device,
Have you ever thought about how secure is it?
So how many valid patterns exist??? any clue?

I was quite curious, so I decided to delve into this puzzle, and wrote a program calculating and demonstrating the number of combinations via Wolfram Mathematica.
The swf clip above was exported from the code I  wrote, pretty neat!
Give it a try and calculate it, you should reach the number 638,600.
I suggest you writing down on paper few basic rules defining a valid sequence, since there are few exceptions.

I'll post next week, my solution and few histograms which will compare the security strength among the three Lock screens (Pattern, PIN , Password).

Have a great week! :-)

Short Tip: 
Try recalling topics taken from Discrete mathematics such as Combinatorics and the principle of inclusion & exclusion.