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A graph is a circle graph if and only if it is the overlap graph of a set of intervals on a line. This is a graph in which the vertices correspond to the intervals, and two vertices are connected by an edge if the two intervals overlap, with neither containing the other. The intersection graph of a set of intervals on a line is called the ...
A pie chart (or a circle chart) is a circular statistical graphic which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area) is proportional to the quantity it represents. While it is named for its resemblance to a pie which has been sliced, there ...
Figure 1: The four charts each map part of the circle to an open interval, and together cover the whole circle. After a line, a circle is the simplest example of a topological manifold. Topology ignores bending, so a small piece of a circle is treated the same as a small piece of a line.
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter.
In graph theory, a circular-arc graph is the intersection graph of a set of arcs on the circle. It has one vertex for each arc in the set, and an edge between every pair of vertices corresponding to arcs that intersect. Formally, let. be a set of arcs. Then the corresponding circular-arc graph is G = (V, E) where. and.
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
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Circulant graphs can be described in several equivalent ways: [2] The automorphism group of the graph includes a cyclic subgroup that acts transitively on the graph's vertices. In other words, the graph has an automorphism which is a cyclic permutation of its vertices. The graph has an adjacency matrix that is a circulant matrix.