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An order-n Venn diagram, for instance, may be viewed as a subdivision drawing of a hypergraph with n hyperedges (the curves defining the diagram) and 2 n − 1 vertices (represented by the regions into which these curves subdivide the plane).
The term "Venn diagram" was later used by Clarence Irving Lewis in 1918, in his book A Survey of Symbolic Logic. [7] [13] In the 20th century, Venn diagrams were further developed. David Wilson Henderson showed, in 1963, that the existence of an n-Venn diagram with n-fold rotational symmetry implied that n was a prime number. [14]
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).
Venn diagram of information theoretic measures for three variables x, y, and z. Each circle represents an individual entropy : H ( x ) {\displaystyle H(x)} is the lower left circle, H ( y ) {\displaystyle H(y)} the lower right, and H ( z ) {\displaystyle H(z)} is the upper circle.
Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article. In terms of a communication channel in which the output Y {\displaystyle Y} is a noisy version of the input X {\displaystyle X} , these relations ...
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
Volcano plots show a characteristic upwards two arm shape because the x axis, i.e. the underlying log 2-fold changes, are generally normal distribution whereas the y axis, the log 10-p values, tend toward greater significance for fold-changes that deviate more strongly from zero. The density of the normal distribution takes the form
A logical graph is a special type of graph-theoretic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic.. In his papers on qualitative logic, entitative graphs, and existential graphs, Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.