graph

See also:Graphand-graph

English

EnglishWikipediahas an article on:

Graph

Wikipedia

Etymology

Clippingofgraphic formula.From 1878; verb from 1889.^[1]

Pronunciation

(Received Pronunciation)IPA^(key):/ɡɹɑːf/
(US,Northern England)IPA^(key):/ɡɹæf/
Audio(US): (file)
Rhymes:-ɑːf,-æf

Noun

graph(pluralgraphs)

(applied mathematics,statistics)Adatachart(graphical representation of data) intended to illustrate therelationshipbetween a set (or sets) of numbers (quantities,measurementsorindicativenumbers) 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
- 2012March,Brian Hayes,“Pixels or Perish”, inAmerican Scientist‎^[1],volume100,number 2, archived fromthe originalon19 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.
(mathematics)A set of points constituting a graphical representation of areal function;(formally)a set oftuples $(x_{1},x_{2},\ldots,x_{m},y)\in \mathbb {R} ^{m+1}$ $(x_{1},x_{2},\ldots ,x_{m},y)\in \mathbb {R} ^{m+1}$ ,where $y=f(x_{1},x_{2},\ldots,x_{m})$ $y=f(x_{1},x_{2},\ldots ,x_{m})$ for a given function $f:\mathbb {R} ^{m}\rightarrow \mathbb {R}$ $f:\mathbb {R} ^{m}\rightarrow \mathbb {R}$ .See alsoGraph of a functionon Wikipedia.Wikipedia
- 1969[MIT Press], Thomas Walsh, Randell Magee (translators), I. M. Gelfand, E. G. Glagoleva, E. E. Shnol,Functions andGraphs,2002, Dover,page 19,
  Let us take any point of the firstgraph,for example, $\textstyle x={\frac {1}{2}},y={\frac {4}{5}}$ ,that is, the point $\textstyle M_{1}({\frac {1}{2}},{\frac {4}{5}})$ .
(graph theory)A set ofvertices(ornodes) connected together byedges;(formally)anordered pairof sets $(V,E)$ $(V,E)$ ,where theelementsof $V$ $V$ are calledverticesornodesand $E$ $E$ is a set of pairs (callededges) of elements of $V$ $V$ .See alsoGraph (discrete mathematics)on Wikipedia.Wikipedia
Hyponyms:directed graph,undirected graph,tree
- 1973,Edward Minieka (translator),Claude Berge,Graphsand Hypergraphs,Elsevier (North-Holland), [1970, Claude Berge,Graphes et Hypergraphes],page vii,
  Problems involvinggraphsfirst appeared in the mathematical folklore as puzzles (e.g. Königsberg bridge problem). Later,graphsappeared 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:
  Spectralgraphtheory 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 treatinggraphswhich are regular and symmetric.
(topology)Atopological spacewhich represents some graph (ordered pair of sets) and which is constructed by representing theverticesaspointsand theedgesas 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 particulartopologycalled thegraph topology.
Synonym: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. Agraph $\Delta$ is a 1-dimensional stratified topological space with finitely many 0-strata (vertices) and finitely many 1-strata (edges).[…]Agraphsuch that any vertex belongs to at least two half-edges we call ans-graph.Clearly the boundary $\partial \Omega$ of a surface $\Omega$ with marked points is an s-graph.
  
  A morphism ofgraphs $\varphi:\Delta '\rightarrow \Delta ''$ is a continuous epimorphic map ofgraphscompatible 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)Amorphism $\Gamma _{f}$ from thedomainof $f$ to theproductof the domain andcodomainof $f$ ,such that the first projection applied to $\Gamma _{f}$ equals theidentityof the domain, and the second projection applied to $\Gamma _{f}$ is equal to $f$ .
(linguistics,typography)Agraphicalunit on thetoken-level,theabstractedfundamental shape of acharacterorletteras distinct from itsductus(realization in a particular typeface or handwriting on theinstance-level) and as distinct by agraphemeon thetype-levelby not fundamentally distinguishingmeaning.
Synonym:glyph
- 2003,J. Richard Andrews,Introduction to Classical Nahuatl, Revised Edition,University of Oklahoma Press, page10:
  Agraphis 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

In mathematics, thegraphical representation of a functionsense is generally of interest only at an elementary level.
- Nevertheless, the termvertex-edge graphis 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).
  - Thefunction $f$ is a set ofordered pairs $(x,f(x))$ ,where $x=(x_{1},x_{2},\ldots,x_{n})$ is a point in $\mathbb {R} ^{n}$ and $f(x)$ is a point in $\mathbb {R}$ .
  - Agraphof $f$ is a set ofpoints(represented asn-tuples) $(x_{1},x_{2},\ldots,x_{n},f(x_{1},x_{2},\ldots,x_{n}))\in \mathbb {R} ^{n+1}$ .
(graph theory):
- A graph $G=(V,E)$ $G=(V,E)$ may be defined such that the elements of $E$ $E$ areordered pairsorunorderedpairs.
  - If the pairs are unordered, $G$ may be called anundirected graphand the elements of $E$ are callededges.
  - If the pairs are ordered, $G$ is called adirected graphordigraphand the elements of $E$ may be calledarcs;the notation $G=(V,A)$ is sometimes used.
  - If the two vertices of an edge represent the same point, the edge may be called aloop.

Hyponyms

Derived terms for types of graph

See alsoGraph (discrete mathematics)on Wikipedia.Wikipedia
See alsoThesaurus:graph

Derived terms

some (unsorted) may be hyponyms

Related terms

Translations

chart—seechart

graph of a function

Afrikaans:grafiek
Albanian:grafik(sq)m
Arabic:مُخَطَّط بَيَانِيّm(muḵaṭṭaṭ bayāniyy)
Armenian:գրաֆիկ(hy)(grafik)
Asturian:gráficu(ast)m
Azerbaijani:qrafik
Belarusian:гра́фікm(hráfik),дыягра́маf(dyjahráma)
Bengali:গ্রাফ(graph)
Bulgarian:гра́фика(bg)f(gráfika),диагра́ма(bg)f(diagráma)
Burmese:ဂရပ်(my)(ga.rap)
Catalan:gràfic(ca)m
Chinese:
Mandarin:Biểu đồ／Biểu đồ(zh)(túbiǎo)
Czech:graf(cs)m
Danish:graf(da)c
Dutch:grafiek(nl)
Esperanto:grafeo
Estonian:graafik
Finnish:diagrammi(fi),kaaviokuva
French:graphique(fr)m
Galician:gráfico(gl)m
Georgian:გრაფიკი(grapiḳi)
German:Graph(de)m,Funktionsgraphm
Greek:γράφημα(el)n(gráfima)
Hebrew:גְּרָף(he)m(graf)
Hindi:लेखाचित्रm(lekhācitra),ग्राफ़m(grāf)
Hungarian:ábra(hu),grafikon(hu)
Indonesian:grafik(id)
Irish:grafm
Italian:grafico(it)m
Japanese:グラフ(ja)(gurafu),Đồ biểu(ja)(ずひょう, zuhyō)
Kazakh:график(grafik)
Khmer:ពិន្ទុរេខីយ(pintureikhəy)
Korean:그래프(ko)(geuraepeu),도표( biểu đồ )(dopyo)
Kyrgyz:график(ky)(grafik)
Lao:ເສັ້ນສະແດງ(sen sa dǣng),ກຣາຟ(ka rāp)
Latvian:grafsm,grafiksm
Lithuanian:grafasm,grafikasm
Macedonian:графико́нm(grafikón)
Malay:graf(ms)
Maori:kauwhata
Mongolian:
Cyrillic:график(mn)(grafik)

Mongolian:ᠭᠷᠠᠹᠢᠻ(ɣrafik)
Norwegian:
Bokmål:graf(no)m
Persian:نمودار(phát)(nemudâr),گراف(phát)(gerâf)
Polish:wykres(pl)m
Portuguese:gráfico(pt)m
Romanian:grafic(ro)n
Russian:гра́фик(ru)m(gráfik),диагра́мма(ru)f(diagrámma)
Scottish Gaelic:grafm
Serbo-Croatian:
Cyrillic:гра̏фm

Roman:grȁf(sh)m
Slovak:graf(sk)m
Slovene:grafm
Spanish:gráfico(es)m
Swahili:jedwali(sw)
Swedish:diagram(sv)n,graf(sv)c
Tagalog:talangguhit
Tajik:график(tg)(grafik)
Thai:กราฟ(th)(gráaf)
Turkish:grafik(tr)
Turkmen:grafik
Ukrainian:гра́фікm(hráfik),діагра́маf(diahráma)
Urdu:گرافm(grāf)
Uzbek:grafik(uz)
Vietnamese:biểu đồ(vi)
Welsh:graffm

set of vertices connected by edges

Belarusian:графm(hraf)
Bulgarian:графm(graf)
Catalan:graf(ca)m
Chinese:
Mandarin:Đồ／Đồ(zh)(tú),Biểu đồ／Biểu đồ(zh)(túbiǎo)
Czech:graf(cs)m
Danish:graf(da)c
Dutch:graaf(nl)
Finnish:verkko(fi),graafi(fi)
French:graphe(fr)m
German:Graph(de)m
Greek:γράφημα(el)n(gráfima),γράφος(el)m(gráfos)
Hebrew:גְּרָף(he)m(graf)
Hindi:लेखाचित्रm(lekhācitra)
Hungarian:gráf(hu)
Irish:grafm
Italian:grafo(it)m
Japanese:グラフ(ja)(gurafu),Đồ biểu(ja)(ずひょう, zuhyō)
Korean:그래프(ko)(geuraepeu),도표( biểu đồ )(dopyo)
Polish:graf(pl)
Portuguese:grafo(pt)m
Romanian:graf(ro)n
Russian:граф(ru)m(graf)
Serbo-Croatian:
Cyrillic:гра̏фm

Roman:grȁf(sh)m
Slovak:graf(sk)m
Spanish:grafo(es)m
Swedish:graf(sv)c
Thai:กราฟ(th)(gráaf)
Ukrainian:графm(hraf)
Vietnamese:biểu đồ(vi)

Verb

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

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

Synonyms

(draw a graph of):chart,plot

Translations

draw a graph of

Galician:debuxar un gráfico de
Irish:graf
Italian:graficare
Spanish:graficar(es)
Swedish:plotta(sv),rita diagram

References

^Douglas Harper (2001–2024) “graph”,inOnline Etymology Dictionary.

Anagrams

phrag

[1] Douglas Harper (2001–2024) “graph”,inOnline Etymology Dictionary.

[1]

graph

Contents

English

Etymology

Pronunciation

Noun

Usage notes

Hyponyms

Derived terms

Related terms

Translations

Verb

Synonyms

Translations

See also

References

Further reading

Anagrams

Navigation menu

graph

English

Etymology

Pronunciation

Noun

Usage notes

Hyponyms

Derived terms

Related terms

Translations

Verb

Synonyms

Translations

See also

References

Further reading

Anagrams

Navigation menu

Search