graph
Pronunciation
  • (RP) IPA: /ɡɹɑːf/
  • (America, Northern England) IPA: /ɡɹæf/
Noun

graph (plural graphs)

  1. (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
  2. (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 Graphs, 2002, Dover, page 19 ↗,
      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).
  3. (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.
    • 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.
  4. (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 graph \Delta is a 1-dimensional stratified topological space with finitely many 0-strata (vertices) and finitely many 1-strata (edges). […] A graph such that any vertex belongs to at least two half-edges we call an s-graph. Clearly the boundary \partial\Omega of a surface \Omega with marked points is an s-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.
  5. (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.
  6. (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
Translations Translations Verb

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

  1. (transitive) To draw a graph.
  2. (transitive, mathematics) To draw a graph of a function.
Synonyms Translations
  • Italian: graficare
  • Spanish: graficar



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