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graph

From Wiktionary, the free dictionary
See also:Graphand-graph

English

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EnglishWikipedia has an article on:
Wikipedia
Agraph of demographic data

Etymology

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Clipping ofgraphicformula. From 1878; verb from 1889.[1]

Pronunciation

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Noun

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graph (pluralgraphs)

  1. (applied mathematics, statistics) Adatachart (graphical representation of data) intended to illustrate therelationship between a set (or sets) of numbers (quantities,measurements orindicative 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
    • 2012 March,Brian Hayes, “Pixels or Perish”, inAmerican Scientist‎[1], volume100, number 2, archived fromthe original on19 February 2013, page106:
      Drawings and pictures are more than mere ornaments in scientific discourse. Blackboard sketches, geological maps, diagrams of molecular structure, astronomical photographs, MRI images, the many varieties of statistical charts andgraphs: These pictorial devices are indispensable tools for presenting evidence, for explaining a theory, for telling a story.
  2. (mathematics) A set of points constituting a graphical representation of areal function;(formally) a set oftuples(x1,x2,…,xm,y)∈Rm+1{\displaystyle (x_{1},x_{2},\ldots ,x_{m},y)\in \mathbb {R} ^{m+1}}, wherey=f(x1,x2,…,xm){\displaystyle y=f(x_{1},x_{2},\ldots ,x_{m})} for a given functionf:Rm→R{\displaystyle f:\mathbb {R} ^{m}\rightarrow \mathbb {R} }. See alsoGraph of a function on Wikipedia.Wikipedia
  4. (graph theory) A set ofvertices (ornodes) connected together byedges;(formally) anordered pair of sets(V,E){\displaystyle (V,E)}, where theelements ofV{\displaystyle V} are calledvertices ornodes andE{\displaystyle E} is a set of pairs (callededges) of elements ofV{\displaystyle V}. See alsoGraph (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 involvinggraphs 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:
      Spectralgraph theory has a long history. In the early days, matrix theory and linear algebra were used to analyze adjacency matrices ofgraphs. Algebraic methods are especially effective in treatinggraphs which are regular and symmetric.
  5. (topology) Atopological space which represents some graph (ordered pair of sets) and which is constructed by representing thevertices aspoints and theedges as copies of therealinterval [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 particulartopology called thegraph topology.
    Synonym:topological graph
  6. (category theory, of a morphism f) AmorphismΓf{\displaystyle \Gamma _{f}} from thedomain off{\displaystyle f} to theproduct of the domain andcodomain off{\displaystyle f}, such that the first projection applied toΓf{\displaystyle \Gamma _{f}} equals theidentity of the domain, and the second projection applied toΓf{\displaystyle \Gamma _{f}} is equal tof{\displaystyle f}.
  7. (linguistics, typography) Agraphical unit on thetoken-level, theabstracted fundamental shape of acharacter orletter as distinct from itsductus (realization in a particular typeface or handwriting on theinstance-level) and as distinct by agrapheme on thetype-level by not fundamentally distinguishingmeaning.
    Synonym:glyph
    • 2003, J. Richard Andrews,Introduction to Classical Nahuatl, Revised Edition, University of Oklahoma Press, page10:
      Agraph is a token-level nondistinctive representation of a grapheme. It can differ from the other variants of its grapheme with regard to upper case, lower case, script, print, typeface style, typeface size, etc.

Usage notes

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  • In mathematics, thegraphical representation of a function sense is generally of interest only at an elementary level. Nevertheless, the termvertex-edge graph is sometimes used in educational texts to distinguish the graph theory sense.

Hyponyms

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Derived terms for types of graph

Derived terms

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some (unsorted) may be hyponyms

Related terms

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Translations

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chart—seechart
graph of a function
set of vertices connected by edges

Verb

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graph (third-person singular simple presentgraphs,present participlegraphing,simple past and past participlegraphed)

  1. (transitive) To draw a graph, to record graphically.
    • 2011,Carlton Mellick III,Crab Town, Portland: Eraserhead Press,→ISBN, page 8:
      When the doctor took the picture that was to begraphed onto Johnny’s balloon head, he suggested that Johnny make a normal face, without expressing any emotion. But Johnny didn’t like that idea. He’d rather look eternally cheerful than express nothing but apathy for the rest of his life.
  2. (transitive, mathematics) To draw a graph of a function.

Synonyms

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Translations

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draw a graph of

See also

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References

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  1. ^Douglas Harper (2001–2025) “graph”, inOnline Etymology Dictionary.

Anagrams

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