there IS an elder wand, dumbledore's wand; which he took from the other dark wizard (dont feel like looking up his name to spell it correctly). but, heres how it goes:

1. draco disarms dumbledore of his wand, meaning it automatically belongs to draco, because disarming means defeating, and the wand changes ownership after an L.

2. right after dumbledore is disarmed, hes killed by snape, but the transfer of ownership is automatic, meaning, that it still belongs to draco. snape would have to defeat draco to claim ownership.

3. dumbledore is buried with the actual wand, but ownership belongs to draco, he just doesnt know it.

4. at malfoy manor, harry takes dracos wand (the one that he bought at the wand shop before starting hogwarts), meaning draco was defeated. this means that he not only physically has dracos wand, it also means that ownership of the elder wand has been passed onto harry (even though its still buried with dumbledore).

5. Riddle takes the wand (physically) from dumbledores grave, but does not know that ownership belongs to harry.

6. Riddle kills snape thinking that ownership will move to him, since he assumed snape was the owner since he killed dumbledore, but after reviewing point 1, we know this isnt true.

7. Riddle tries to kill harry, but the wand realizes that harry is the true owner and thus, backfires.

-hope that helps