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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.
A circle of radius 23 drawn by the Bresenham algorithm. In computer graphics, the midpoint circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. It is a generalization of Bresenham's line algorithm. The algorithm can be further generalized to conic sections. [1] [2] [3]
With an additional (free) package, it's also possible to generate SVG-graphs with R directly. See an example with code on Image:Circle area Monte Carlo integration2.svg. Other packages (lattice, ggplot2) provide alternative graphics facilities or syntax. Here is another example with data.
Perfect matchings may be described in several other equivalent ways, including involutions without fixed points on a set of n + 1 items (permutations in which each cycle is a pair) [1] or chord diagrams (sets of chords of a set of n + 1 points evenly spaced on a circle such that each point is the endpoint of exactly one chord, also called ...
As another example, the "average time" between 11 PM and 1 AM is either midnight or noon, depending on whether the two times are part of a single night or part of a single calendar day. The circular mean is one of the simplest examples of directional statistics and of statistics of non-Euclidean spaces. This computation produces a different ...
A simple decision tree to detect the presence of a 3-clique in a 4-vertex graph. It uses up to 6 questions of the form "Does the red edge exist?", matching the optimal bound n(n − 1)/2. The (deterministic) decision tree complexity of determining a graph property is the number of questions of the form "Is there an edge between vertex u and ...
Example of a positive reinforcing loop between two values: bank balance and earned interest. A causal loop diagram (CLD) is a causal diagram that visualizes how different variables in a system are causally interrelated. The diagram consists of a set of words and arrows.
A circle with five chords and the corresponding circle graph. In graph theory, a circle graph is the intersection graph of a chord diagram.That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.