noun

• (geometry, physics, engineering, of an object or a geometrical figure) The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.
• (geometry, specifically, of a triangle) The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.
• (of a finite set of points) the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.
• (mathematical analysis, of a function) An analogue of the centre of gravity of a nonuniform body in which local density is replaced by a specified function (which can take negative values) and the place of the body's shape is taken by the function's domain.
• (statistics, cluster analysis, of a cluster of points) the arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.
• (graph theory, of a tree) Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.