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Chord diagrams are conventionally visualized by arranging the objects in their order around a circle, and drawing the pairs of the matching as chords of the circle. The number of different chord diagrams that may be given for a set of 2 n {\displaystyle 2n} cyclically ordered objects is the double factorial ( 2 n − 1 ) ! ! {\displaystyle (2n ...
A chord diagram is a graphical method of displaying the inter-relationships between data in a matrix. The data are arranged radially around a circle with the relationships between the data points typically drawn as arcs connecting the data. The format can be aesthetically pleasing, making it a popular choice in the world of data visualization.
Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).
Chordal graphs are a subclass of the well known perfect graphs. Other superclasses of chordal graphs include weakly chordal graphs, cop-win graphs, odd-hole-free graphs, even-hole-free graphs, and Meyniel graphs. Chordal graphs are precisely the graphs that are both odd-hole-free and even-hole-free (see holes in graph theory).
The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
A chord diagram may refer to: Chord diagram (music) , a diagram showing the fingering of a chord on a guitar or other fretted musical instrument Chord diagram (information visualization) , a diagram showing a many-to-many relationship between objects as curved arcs within a circle
The expression () gives the slope of the line joining the points (, ()) and (, ()), which is a chord of the graph of , while ′ gives the slope of the tangent to the curve at the point (, ()). Thus the mean value theorem says that given any chord of a smooth curve, we can find a point on the curve lying between the end-points of the chord such ...
A graph is a permutation graph if and only if is a circle graph that admits an equator, i.e., an additional chord that intersects every other chord. [ 2 ] A graph G {\displaystyle G} is a permutation graph if and only if both G {\displaystyle G} and its complement G ¯ {\displaystyle {\overline {G}}} are comparability graphs .
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