English
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.
    Hyponyms: bar graph, line graph, pie graph
  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. See also w:Graph of a function on Wikipedia.Wikipedia
    • 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) A set of vertices (or nodes) connected together by edges; (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. See also w:Graph (discrete mathematics) on Wikipedia.Wikipedia
    Hyponyms: directed graph, undirected graph, tree
    • 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.
  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; simple past and past participle graphed)

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


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