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graph, figure that shows relationships between quantities. The graph of a function *y*=*f* (*x*) is the set of points with coordinates [*x, f* (*x*)] in the *xy*-plane, when *x* and *y* are numbers. A similar definition can be given for functions involving more general kinds of variables. In mathematics interest is almost exclusively in line graphs and what these reveal about the functions they represent. Statistics makes extensive use of both line graphs and bar graphs, in which the lengths of the various bars show the quantities to be compared. Graph is also a mathematical term used in combinatorics to designate a geometric object consisting of vertices and edges (joining pairs of vertices). Such objects have been studied considerably in recent years because of the applicability to such diverse fields as computer networks, game theory, and social psychology.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

Mathematical theory of networks. A graph consists of vertices (also called points or nodes) and edges (lines) connecting certain pairs of vertices. An edge that connects a node to itself is called a loop. In 1735 Leonhard Euler published an analysis of an old puzzle concerning the possibility of crossing every one of seven bridges (no bridge twice) that span a forked river flowing past an island. Euler's proof that no such path exists and his generalization of the problem to all possible networks are now recognized as the origin of both graph theory and topology. Since the mid-20th century, graph theory has become a standard tool for analyzing and designing communications networks, power transmission systems, transportation networks, and computer architectures.

Learn more about graph theory with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Visual representation of a data set or a mathematical equation, inequality, or function to show relationships or tendencies that these formulas can only suggest symbolically and abstractly. Though histograms and pie charts are also graphs, the term usually applies to point plots on a coordinate system. For example, a graph of the relationship between real numbers and their squares matches each real number on a horizontal axis with its square on a vertical axis. The resulting set of points in this case is a parabola. A graph of an inequality is usually a shaded region on one side of a curve, whose shape depends not only on the equation or inequality but on the coordinate system chosen.

Learn more about graph with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Graph may refer to:### See also

- A graphic (such as a chart or diagram) depicting the relationship between two or more variables used, for instance, in visualising scientific data.

In mathematics:

- Graph (mathematics), a set of vertices connected with edges
- Graph theory
- Graph of a function f : X → Y:

In computer science:

- Graph (data structure), an abstract data type representing relationships or connections
- Graph (software), the name of a software application for mathematical plotting

Other uses:

- HMS Graph (P715), a submarine of the Royal Navy (United Kingdom)

- Grapheme (linguistics)
- -graphy (suffix)
- Graf
- Graff
- List of graphing software

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Last updated on Wednesday October 08, 2008 at 13:07:32 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Wednesday October 08, 2008 at 13:07:32 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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