WordNet sense 1 ((football) the person who plays center on the line of scrimmage and snaps the ball to the quarterback):

snapper

WordNet sense 2 (an area that is approximately central within some larger region):

eye, heart, middle, centre

WordNet sense 3 (a point equidistant from the ends of a line or the extremities of a figure):

midpoint

WordNet sense 4 (the choicest or most essential or most vital part of some idea or experience):

core, essence, gist, kernel, marrow, meat, nitty-gritty, nub, pith, substance, sum, inwardness, heart and soul

WordNet sense 5 (the object upon which interest and attention focuses):

center of attention

WordNet sense 6 (a cluster of nerve cells governing a specific bodily process):

nerve center, nerve centre

WordNet sense 7 (mercantile establishment consisting of a carefully landscaped complex of shops representing leading merchandisers; usually includes restaurants and a convenient parking area; a modern version of the traditional marketplace):

mall, plaza, shopping centre, shopping mall, shopping center

WordNet sense 8 (the piece of ground in the outfield directly ahead of the catcher):

center field, centerfield

WordNet sense 9 (center upon):

revolve around, focus on, center on, concentrate on, revolve about

WordNet sense 10 (direct one's attention on something):

concentrate, focus, pore, rivet

WordNet sense 11 (equally distant from the extremes):

halfway, midway

WordNet sense 12 (in or near a center or constituting a center; the inner area):

central