A special formation in which the player snapping the ball is lined up on one end of the line of scrimmage, thus making him an eligible receiver. This formation is seen very rarely in professional football, and is only considered useful in the event of a trick play of some time. A formation like a center eligible is seen more often at the amateur levels due to the likelihood of a team being confused by the strange formation.
Also known as "Snapper Eligible"
Formations like the center eligible are quite rare due to the complexities of the rules regarding eligible players and formations. Teams are required to have a certain number of players on the line of scrimmage prior to a play, and those players have to have certain uniform numbers. Offensive linemen are required to wear numbers between 50 and 79. A team utilizing a center eligible is likely to attempt to run some manner of misdirection play, since the offensive line would be significantly unbalanced by having the snapper on one side of the line.