Encyclopedia > Diameter

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The diameter of a circle is the length of a straight line segment that passes from a point on the circle to the opposite point (and therefore passes through the centre of the circle). This length is twice the radius. The line segment itself is also called a diameter.

The diameter of a connected graph is the distance between the two vertices which are furthest from each other. The distance between two vertices a and b is the length of the shortest path connecting them (for the length of a path, see Graph theory).

The two definitions given above are special cases of a more general definition. The diameter of a subset of a metric space is the least upper bound of the distances between pairs of points in the subset. So, if A is the subset, the diameter is

sup { d(x, y) | x, y in A }.

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