View source for Graph

{{also|Graph|-graph}}
==English==
{{wikipedia|Graph}}
[[File:Demography graphic of Pichilemu.png|thumb|A '''graph''' of demographic data]]

===Etymology===
{{root|en|ine-pro|*gerbʰ-}}
{{clipping|en|[[graphic]] [[formula]]}}. From 1878; verb from 1889.<ref>{{R:Etymonline}}</ref>

===Pronunciation===
* {{IPA|en|/ɡɹɑːf/|a=RP}}
* {{IPA|en|/ɡɹæf/|a=US,Northern England}}
* {{audio|en|en-us-graph.ogg|a=US}}
* {{rhymes|en|ɑːf|æf|s=1}}

===Noun===
{{en-noun}}

# {{lb|en|applied mathematics|statistics}} A [[data]] [[chart]] (graphical representation of data) intended to illustrate the [[relationship]] between a set (or sets) of numbers ([[quantity|quantities]], [[measurement]]s 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|bar graph|line graph|pie graph}}
#* {{quote-journal
|1=en
|date=2012-03
|author=[[w:Brian Hayes (scientist)|Brian Hayes]]
|title=Pixels or Perish
|volume=100
|issue=2
|page=106
|magazine=w:American Scientist
|url=http://www.americanscientist.org/issues/pub/pixels-or-perish
|passage=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 and '''graphs''': These pictorial devices are indispensable tools for presenting evidence, for explaining a theory, for telling a story.
|accessdate=15 May 2013
|archiveurl=https://web.archive.org/web/20130219223150/http://www.americanscientist.org/issues/pub/pixels-or-perish
|archivedate=19 February 2013
}}
# {{lb|en|mathematics}} A set of points constituting a graphical representation of a [[real function]]; {{lb|en|formally}} a set of [[tuple]]s <math>(x_1, x_2, \ldots, x_m, y)\in\R^{m+1}</math>, where <math>y=f(x_1, x_2, \ldots, x_m)</math> for a given function <math>f: \R^m\rightarrow\R</math>. See also {{pedia|Graph of a function}} {{C|en|Curves}} {{C|en|Functions}}
#* '''1969''' [MIT Press], Thomas Walsh, Randell Magee (translators), I. M. Gelfand, E. G. Glagoleva, E. E. Shnol, ''Functions and '''Graphs''''', 2002, Dover, [https://books.google.com.au/books?id=5GTDAgAAQBAJ&printsec=frontcover&dq=%22graph%22%7C%22graphs%22&hl=en&sa=X&ved=0ahUKEwjoo9Tsi5feAhWwHDQIHe6XANYQ6AEI5gEwHQ#v=onepage&q=%22graph%22%7C%22graphs%22&f=false page 19],
#*: Let us take any point of the first '''graph''', for example, <math>\textstyle x=\frac 1 2, y=\frac 4 5</math>, that is, the point <math>\textstyle M_1(\frac 1 2,\frac 4 5)</math>.
# {{lb|en|graph theory}} A set of ''vertices'' (or ''nodes'') connected together by ''edges''; {{lb|en|formally}} an [[ordered pair]] of sets <math>(V,E)</math>, where the [[element]]s of <math>V</math> are called ''[[vertex|vertices]]'' or ''[[node]]s'' and <math>E</math> is a set of pairs (called ''[[edge]]s'') of elements of <math>V</math>. See also {{pedia|Graph (discrete mathematics)}}
#: {{hypo|en|directed graph|undirected graph|tree}}
#* '''1973''', Edward Minieka (translator), {{w|Claude Berge}}, '''''Graphs''' and Hypergraphs'', Elsevier (North-Holland), [1970, Claude Berge, ''Graphes et Hypergraphes''], [https://books.google.com.au/books?id=Wy2mhanRnk4C&pg=PR7&dq=%22graph%22%7C%22graphs%22+%22category+theory%22&hl=en&sa=X&ved=0ahUKEwj1opeLjJfeAhUiFzQIHVfGDP8Q6AEIZzAL#v=onepage&q=%22graph%22%7C%22graphs%22%20%22category%20theory%22&f=false 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.
#* {{quote-book|en|year=1997|author=Fan R. K. Chung|title=Spectral Graph Theory|publisher=w:American Mathematical Society|pageurl=https://books.google.com.au/books?id=YUc38_MCuhAC&printsec=frontcover&dq=%22graph%22%7C%22graphs%22&hl=en&sa=X&ved=0ahUKEwjoo9Tsi5feAhWwHDQIHe6XANYQ6AEIzgIwLQ#v=onepage&q=%22graph%22%7C%22graphs%22&f=false|page=1
|passage=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.}}
# {{lb|en|topology}} A [[topological space]] which represents some graph (ordered pair of sets) and which is constructed by representing the ''vertices'' as ''[[point]]s'' and the ''edges'' as copies of the [[real numbers|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]]''.
#: {{syn|en|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'', {{w|American Mathematical Society}}, [https://books.google.com.au/books?id=zjrHDWkVKvoC&pg=PA6&dq=%22graph%22%7C%22graphs%22+topology&hl=en&sa=X&ved=0ahUKEwjQta7r3pneAhWoGDQIHX8rDvsQ6AEIdjAN#v=onepage&q=%22graph%22%7C%22graphs%22%20topology&f=false page 6],
#*: First, let us define its 1-dimensional analog, that is, a topological graph. A '''''graph''''' <math>\Delta</math> 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 <math>\partial\Omega</math> of a surface <math>\Omega</math> with marked points is an s-'''graph'''.
#*: A morphism of '''graphs''' <math>\varphi: \Delta'\rightarrow\Delta''</math> is a continuous epimorphic map of '''graphs''' compatible with the stratification; i.e., the restriction of <math>\varphi</math> to any open 1-stratum (interior of an edge) of <math>\Delta'</math> is a local (therefore, global) homeomorphism with appropriate open 1-stratum of <math>\Delta''</math>.
# {{lb|en|category theory|of a morphism f}} A [[morphism]] <math>\Gamma_f</math> from the [[domain]] of <math>f</math> to the [[categorical product|product]] of the domain and [[codomain]] of <math>f</math>, such that the first projection applied to <math>\Gamma_f</math> equals the [[identity morphism|identity]] of the domain, and the second projection applied to <math>\Gamma_f</math> is equal to <math>f</math>.
# {{lb|en|linguistics|typography}} A [[graphical]] unit on the {{l|en|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 {{l|en|instance-level}}) and as distinct by a {{l|en|grapheme}} on the {{l|en|type-level}} by not fundamentally distinguishing {{l|en|meaning}}.
#: {{syn|en|glyph}}
#* {{quote-book|en|author=J. Richard Andrews|year=2003|title=Introduction to Classical Nahuatl, Revised Edition|page=10|publisher=University of Oklahoma Press|passage=A '''''graph''''' <!--- bold and italic in the source ---> 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====
* In mathematics, the ''graphical representation of a function'' sense is generally of interest only at an elementary level. Nevertheless, the term {{m|en|vertex-edge graph}} is sometimes used in educational texts to distinguish the graph theory sense.

====Hyponyms====
{{col4|en|acyclic graph|biased graph|biconnected graph|bipartite graph|complete graph|connected graph|dependency graph|digraph|directed graph|Eulerian graph|Hamiltonian graph|line graph|multigraph|nonoriented graph|object graph|oriented graph|Petersen graph|pseudograph|random graph|regular graph|signed graph|small world graph|strongly regular graph|subgraph|superregular graph|undirected graph|Heawood graph|Keller graph|polygon-circle graph|Ramanujan graph|unicursal graph|voltage graph|flame graph|weighted graph|control-flow graph|circular graph|diamond graph|functional graph|Grötzsch graph|Kneser graph|Meyniel graph|Mycielski graph|scene graph|theta graph|windmill graph|Yao graph|title=Derived terms for types of graph}}
* See also [[Thesaurus:graph]]

====Derived terms====
{{col4|en|title=some (unsorted) may be hyponyms|conceptual graph|graph centre|graph eccentricity|graph eigenvalue|graph geodesic|graph minor|graph paper|graph polynomial|graph spectrum|graph thickness|graph topology|graphic matroid|graphoid|hypergraph|topological graph|algebraic graph theory|block graph|brain graph|bullet graph|call graph|Cayley graph|cherry graph|cocktail party graph|complete bipartite graph|Coxeter graph|crown graph|cubic graph|de Bruijn graph|Desargues graph|directed acyclic graph|directed acyclic word graph|dual graph|empty graph|factor graph|graph antihole|graph hole|graph state|graph theorist|graph toughness|graph-theoretic|graph-theoretical|graph-theoretically|Herschel graph|knowledge graph|Levi graph|medial graph|Moore graph|planar graph|plane graph|social graph|spider graph|stream graph|Tanner graph|Turán graph|utility graph|Laves graph|bigraph|braingraph|cograph|elastograph|ergograph|fatgraph|flowgraph|fluviograph|gastrograph|graphable|graphiology|graphlet|graphlike|graphon|graphophone|graphwork|hypograph|integraph|karyograph|logograph|metagraph|phenograph|protograph|rectagraph|regraph|scenegraph|sonograph|spirograph|streamgraph|supergraph|telegraph|termgraph|ultragraph|viewgraph|graph homomorphism}}

====Related terms====
{{col3
|en|grapheme
|graphic
|graphical
|graphism
}}

====Translations====
{{trans-see|chart}}
{{trans-top|graph of a function}}
* Afrikaans: {{t|af|grafiek}}
* Albanian: {{t+|sq|grafik|m}}
* Arabic: {{t|ar|مُخَطَّط بَيَانِيّ|m}}
* Armenian: {{t+|hy|գրաֆիկ}}
* Asturian: {{t+|ast|gráficu|m}}
* Azerbaijani: {{t|az|qrafik}}
* Belarusian: {{t|be|гра́фік|m}}, {{t|be|дыягра́ма|f}}
* Bengali: {{t|bn|গ্রাফ}}
* Bulgarian: {{t+|bg|гра́фика|f}}, {{t+|bg|диагра́ма|f}}
* Burmese: {{t+|my|ဂရပ်}}
* Catalan: {{t+|ca|gràfic|m}}
* Chinese:
*: Mandarin: {{t+|cmn|圖表|tr=túbiǎo}}
* Czech: {{t+|cs|graf|m}}
* Danish: {{t+|da|graf|c}}
* Dutch: {{t+|nl|grafiek|f}}
* Esperanto: {{t|eo|grafeo}}
* Estonian: {{t|et|graafik}}
* Finnish: {{t+|fi|diagrammi}}, {{t|fi|kaaviokuva}}
* French: {{t+|fr|graphique|m}}
* Galician: {{t+|gl|gráfico|m}}
* Georgian: {{t|ka|გრაფიკი}}
* German: {{t+|de|Graph|m}}, {{t|de|Funktionsgraph|m}}
* Greek: {{t+|el|γράφημα|n}}
* Hebrew: {{t+|he|גְּרָף|m|tr=graf}}
* Hindi: {{t|hi|लेखाचित्र|m}}, {{t|hi|ग्राफ़|m}}
* Hungarian: {{t+|hu|ábra}}, {{t+|hu|grafikon}}
* Indonesian: {{t+|id|grafik}}
* Irish: {{t|ga|graf|m}}
* Italian: {{t+|it|grafico|m}}
* Japanese: {{t+|ja|グラフ|tr=gurafu}}, {{t+|ja|図表|tr=ずひょう, zuhyō}}
* Kazakh: {{t|kk|график}}
* Khmer: {{t|km|ពិន្ទុរេខីយ}}
* Korean: {{t+|ko|그래프}}, {{t|ko|도표(圖表)}}
* Kyrgyz: {{t+|ky|график}}
* Lao: {{t|lo|ເສັ້ນສະແດງ}}, {{t|lo|ກຣາຟ}}
* Latvian: {{t|lv|grafs|m}}, {{t|lv|grafiks|m}}
* Lithuanian: {{t|lt|grafas|m}}, {{t|lt|grafikas|m}}
* Macedonian: {{t|mk|графико́н|m}}
* Malay: {{t+|ms|graf}}
* Maori: {{t|mi|kauwhata}}
* Mongolian:
*: Cyrillic: {{t+|mn|график}}
*: Mongolian: {{t|mn|ᠭᠷᠠᠹᠢᠻ}}
* Norwegian:
*: Bokmål: {{t+|nb|graf|m}}
* Persian: {{t+|fa|نمودار|tr=nemudâr}}, {{t+|fa|گراف|tr=gerâf}}
* Polish: {{t+|pl|wykres|m}}
* Portuguese: {{t+|pt|gráfico|m}}
* Romanian: {{t+|ro|grafic|n}}
* Russian: {{t+|ru|гра́фик|m}}, {{t+|ru|диагра́мма|f}}
* Scottish Gaelic: {{t|gd|graf|m}}
* Serbo-Croatian:
*: Cyrillic: {{t|sh|гра̏ф|m}}
*: Roman: {{t+|sh|grȁf|m}}
* Slovak: {{t+|sk|graf|m}}
* Slovene: {{t|sl|graf|m}}
* Spanish: {{t+|es|gráfico|m}}
* Swahili: {{t+|sw|jedwali}}
* Swedish: {{t+|sv|diagram|n}}, {{t+|sv|graf|c}}
* Tagalog: {{t|tl|talangguhit}}
* Tajik: {{t+|tg|график}}
* Thai: {{t+|th|กราฟ}}
* Turkish: {{t+|tr|grafik}}
* Turkmen: {{t|tk|grafik}}
* Ukrainian: {{t|uk|гра́фік|m}}, {{t|uk|діагра́ма|f}}
* Urdu: {{t|ur|گراف|m|tr=grāf}}
* Uzbek: {{t+|uz|grafik}}
* Vietnamese: {{t+|vi|biểu đồ}}
* Welsh: {{t|cy|graff|m}}
{{trans-bottom}}

{{trans-top|set of vertices connected by edges}}
* Belarusian: {{t|be|граф|m}}
* Bulgarian: {{t|bg|граф|m}}
* Catalan: {{t+|ca|graf|m}}
* Chinese:
*: Mandarin: {{t+|cmn|圖|tr=tú}}, {{t+|cmn|圖表|tr=túbiǎo}}
* Czech: {{t+|cs|graf|m}}
* Danish: {{t+|da|graf|c}}
* Dutch: {{t+|nl|graaf|m}}
* Finnish: {{t+|fi|verkko}}, {{t+|fi|graafi}}
* French: {{t+|fr|graphe|m}}
* German: {{t+|de|Graph|m}}
* Greek: {{t+|el|γράφημα|n}}, {{t+|el|γράφος|m}}
* Hebrew: {{t+|he|גְּרָף|m|tr=graf}}
* Hindi: {{t|hi|लेखाचित्र|m}}
* Hungarian: {{t+|hu|gráf}}
* Irish: {{t|ga|graf|m}}
* Italian: {{t+|it|grafo|m}}
* Japanese: {{t+|ja|グラフ|tr=gurafu}}, {{t+|ja|図表|tr=ずひょう, zuhyō}}
* Korean: {{t+|ko|그래프}}, {{t|ko|도표(圖表)}}
* Polish: {{t+|pl|graf}}
* Portuguese: {{t+|pt|grafo|m}}
* Romanian: {{t+|ro|graf|n}}
* Russian: {{t+|ru|граф|m}}
* Serbo-Croatian:
*: Cyrillic: {{t|sh|гра̏ф|m}}
*: Roman: {{t+|sh|grȁf|m}}
* Slovak: {{t+|sk|graf|m}}
* Spanish: {{t+|es|grafo|m}}
* Swedish: {{t+|sv|graf|c}}
* Thai: {{t+|th|กราฟ}}
* Ukrainian: {{t|uk|граф|m}}
* Vietnamese: {{t+|vi|biểu đồ}}
{{trans-bottom}}

===Verb===
{{en-verb}}

# {{lb|en|transitive}} To draw a graph, to record graphically.
#* {{quote-book|en|year=2011|title=Crab Town|author={{w|Carlton Mellick III}}|isbn=1-936383-41-1|location=Portland|publisher=Eraserhead Press|page=8|passage=When the doctor took the picture that was to be '''graphed''' 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.}}
# {{lb|en|transitive|mathematics}} To draw a graph of a function.

====Synonyms====
* {{sense|draw a graph of}} {{l|en|chart}}, {{l|en|plot}}

====Translations====
{{trans-top|draw a graph of}}
* Galician: {{t|gl|debuxar un gráfico de}}
* Irish: {{t|ga|graf}}
* Italian: {{t|it|graficare}}
* Spanish: {{t+|es|graficar}}
* Swedish: {{t+|sv|plotta}}, {{t|sv|rita diagram}}
{{trans-bottom}}

===See also===
* [http://mathworld.wolfram.com/Graph.html Graph] on {{w|MathWorld|Wolfram MathWorld}}

===References===
<references />

===Anagrams===
* {{anagrams|en|a=aghpr|phrag}}

{{C|en|Visualization}}