GRAPH

character, graph, grapheme, graphic symbol

(noun) a written symbol that is used to represent speech; “the Greek alphabet has 24 characters”

chart, graph

(noun) a visual display of information

graph, graphical record, graphical recording

(noun) a visual representation of the relations between certain quantities, represented as points, plotted with reference to a set of axes

graph, chart

(verb) represent by means of a graph; “chart the data”

graph

(verb) plot upon a graph

Source: WordNet® 3.1

Etymology

Noun

graph (plural graphs)

(applied mathematics, statistics) A data chart (graphical representation of data) intended to illustrate the relationship between a set (or sets) of numbers (quantities, measurements or indicative numbers) and a reference set, whose elements are indexed to those of the former set(s) and may or may not be numbers.

Hyponyms: bar graph, line graph, pie graph

(mathematics) A set of points constituting a graphical representation of a real function; (formally) a set of tuples $$(x_1, x_2, \ldots, x_m, y)\in\R^{m+1}$$ , where $$y=f(x_1, x_2, \ldots, x_m)$$ for a given function $$f: \R^m\rightarrow\R$$ .

(graph theory) (formally) An ordered pair of sets $$(V,E)$$ , where the elements of $$V$$ are called vertices or nodes and $$E$$ is a set of pairs (called edges) of elements of $$V$$ ; (less formally) a set of vertices (or nodes) together with a set of edges that connect (some of) the vertices.

Hyponyms: directed graph, undirected graph, tree

(topology) A topological space which represents some graph (ordered pair of sets) and which is constructed by representing the vertices as points and the edges as copies of the real interval [0,1] (where, for any given edge, 0 and 1 are identified with the points representing the two vertices) and equipping the result with a particular topology called the graph topology.

Synonym: topological graph

A morphism of graphs $$\varphi: \Delta'\rightarrow\Delta$ $ is a continuous epimorphic map of graphs compatible with the stratification; i.e, the restriction of $$\varphi$$ to any open 1-stratum (interior of an edge) of $$\Delta'$$ is a local (therefore, global) homeomorphism with appropriate open 1-stratum of $$\Delta$ $.

(category theory, of a morphism f) A morphism $$\Gamma_f$$ from the domain of $$f$$ to the product of the domain and codomain of $$f$$ , such that the first projection applied to $$\Gamma_f$$ equals the identity of the domain, and the second projection applied to $$\Gamma_f$$ is equal to $$f$$ .

(linguistics, typography) A graphical unit on the token-level, the abstracted fundamental shape of a character or letter as distinct from its ductus (realization in a particular typeface or handwriting on the instance-level) and as distinct by a grapheme on the type-level by not fundamentally distinguishing meaning.

Synonym: glyph

Usage notes

• In mathematics, the graphical representation of a function sense is generally of interest only at an elementary level.

Nevertheless, the term vertex-edge graph is sometimes used in educational texts to distinguish the graph theory sense.

• (points constituting a graphical representation of a function)

A graph is similar to, but not the same as a (real) function (as defined formally).

The function $$f$$ is a set of ordered pairs $$(x, f(x))$$ , where $$x=(x_1, x_2, \ldots, x_n)$$ is a point in $$\R^n$$ and $$f(x)$$ is a point in $$\R$$ .

A graph of $$f$$ is a set of points (represented as n-tuples) $$(x_1, x_2, \ldots, x_n, f(x_1, x_2, \ldots, x_n))\in\R^{n+1}$$ .

• (graph theory)

A graph $$G=(V,E)$$ may be defined such that the elements of $$E$$ are ordered pairs or unordered pairs.

If the pairs are unordered, $$G$$ may be called an undirected graph and the elements of $$E$$ are called edges.

If the pairs are ordered, $$G$$ is called a directed graph or digraph and the elements of $$E$$ may be called arcs; the notation $$G=(V,A)$$ is sometimes used.

If the two vertices of an edge represent the same point, the edge may be called a loop.

Hyponyms

(Derived terms for types of graph):

• acyclic graph

• biased graph

• biconnected graph

• bipartite graph

• complete graph

• connected graph

• dependency graph

• directed graph

• Eulerian graph

• Hamiltonian graph

• line graph

• multigraph

• nonoriented graph

• object graph

• oriented graph

• Petersen graph

• pseudograph

• random graph

• regular graph

• signed graph

• small world graph

• strongly regular graph

• subgraph

• superregular graph

• undirected graph

• unicursal graph

• voltage graph

• weighted graph

• See also

• See also graph

Verb

graph (third-person singular simple present graphs, present participle graphing, simple past and past participle graphed)

(transitive) To draw a graph.

(transitive, mathematics) To draw a graph of a function.

Synonyms

• (draw a graph of): chart, plot

Anagrams

• phrag

Source: Wiktionary

-graph ( Etym: [From Gr. gra`fein to write. See Graphic.]

Definition: A suffix signifying something written, a writing; also, a writer; as autograph, crystograph, telegraph, photograph.

Source: Webster’s Unabridged Dictionary 1913 Edition

GRAPH

Etymology

Noun

Usage notes

Hyponyms

Verb

Synonyms

Anagrams

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