An elite player at the end of the first round. Center isn't a position that's normally highly regarded but I think you can justify a first round pick on a center who is considered the best in the class, as Konz is.
SB Nation's Giants blog, Big Blue View, explains the pick:
The Giants could go a lot of different ways here: offensive line, wide receiver, running back, linebacker, and cornerback. Konz seemingly doesn't fill the need for an offensive tackle, but he is the best offensive lineman and best value left on the board. Giants GM Jerry Reese is all about value, so Konz is the choice. Besides, he could end up starting at left guard.