graph

Pronunciation Noun

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Pronunciation 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.*hypo*en

- (
*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.**1969**[MIT Press], Thomas Walsh, Randell Magee (translators), I. M. Gelfand, E. G. Glagoleva, E. E. Shnol,*Functions and*, 2002, Dover, page 19 ↗,**Graphs**- Let us take any point of the first
**graph**, for example, \textstyle x=\frac 1 2, y=\frac 4 5, that is, the point \textstyle M_1(\frac 1 2,\frac 4 5).

- Let us take any point of the first

- (
*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.*hypo*en

**1973**, Edward Minieka (translator), Claude Berge,*Graphs**and Hypergraphs*, Elsevier (North-Holland), [1970, Claude Berge,*Graphes et Hypergraphes*], page vii ↗,- Problems involving
**graphs**first appeared in the mathematical folklore as puzzles (e.g. Königsberg bridge problem). Later,**graphs**appeared in electrical engineering (Kirchhof's Law), chemistry, psychology and economics before becoming a unified field of study.

- Problems involving
**1997**, Fan R. K. Chung,*Spectral Graph Theory*, American Mathematical Society, page 1 ↗,- Spectral
**graph**theory has a long history. In the early days, matrix theory and linear algebra were used to analyze adjacency matrices of**graphs**. Algebraic methods are especially effective in treating**graphs**which are regular and symmetric.

- Spectral

- (
*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*.- Synonyms: topological graph

**2008**, Unnamed translators (AMS), A. V. Alexeevski, S. M. Natanzon,*Hurwitz Numbers for Regular Coverings of Surfaces by Seamed Surfaces and Cardy-Frobenius Algebras of Finite Groups*, V. M. Buchstaber, I. M. Krichever (editors),*Geometry, Topology, and Mathematical Physics: S.P. Novikov's Seminar, 2006-2007*, American Mathematical Society, page 6 ↗,- First, let us define its 1-dimensional analog, that is, a topological graph. A
\Delta is a 1-dimensional stratified topological space with finitely many 0-strata (vertices) and finitely many 1-strata (edges). […] A*graph***graph**such that any vertex belongs to at least two half-edges we call an*s-*. Clearly the boundary \partial\Omega of a surface \Omega with marked points is an s-**graph****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

- First, let us define its 1-dimensional analog, that is, a topological graph. A

- (
*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.- Synonyms: glyph

- French: graphique
- German: Graph, Funktionsgraph
- Italian: grafico
- Portuguese: gráfico
- Russian: гра́фик
- Spanish: gráfico

**graph** (graphs, *present participle* graphing; *past and past participle* graphed)

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

- Italian: graficare
- Spanish: graficar

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.007