graph en · NOUN
Pronunciation
- /ɡɹɑːf/ (Received-Pronunciation)
- (US) audio
- /ɡɹæf/ (Northern-England, US)
- /ɡɹæf/ (Received-Pronunciation)
- /ɡɹɑːf/ (British, Southern, Standard)
- /ɡɹaf/ (British, Southern, Standard)
Etymology
Clipping of graphic formula. From 1878; verb from 1889.
Meanings
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(qualifier:applied mathematics) 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.
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.
2012 March 14, Brian Hayes, “Pixels or Perish”, in American Scientist, volume 100, number 2, archived from the original on 19 Feb 2013, page 106:
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A set of points constituting a graphical representation of a real function; (formally) a set of tuples (x_1,x_2,…,x_m,y)∈ R ᵐ⁺¹, where y=f(x_1,x_2,…,x_m) for a given function f: R ᵐ→ R . See also 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, x=1/2,y=4/5, that is, the point M_1(1/2,4/5).
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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 Graph (discrete mathematics) on Wikipedia.Wikipedia
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.
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.
1997, Fan R. K. Chung, Spectral Graph Theory, American Mathematical Society, page 1:
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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.
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 Δ 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 ∂Ω of a surface Ω with marked points is an s-graph. A morphism of graphs φ:Δ'→Δ is a continuous epimorphic map of graphs compatible with the stratification; i.e., the restriction of φ to any open 1-stratum (interior of an edge) of Δ' is a local (therefore, global) homeomorphism with appropriate open 1-stratum of Δ.
- (of a morphism f) A morphism Γ_f from the domain of f to the product of the domain and codomain of f, such that the first projection applied to Γ_f equals the identity of the domain, and the second projection applied to Γ_f is equal to f.
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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.
A graph 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.
2003, J. Richard Andrews, Introduction to Classical Nahuatl, Revised Edition, University of Oklahoma Press, page 10:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| graphs | Number=Plur | lexicographic |
Deriveds
graphwork (some (unsorted) may be hyponyms) · graph toughness (some (unsorted) may be hyponyms) · cubic graph (some (unsorted) may be hyponyms) · social graph (some (unsorted) may be hyponyms) · bullet graph (some (unsorted) may be hyponyms) · protograph (some (unsorted) may be hyponyms) · ultragraph (some (unsorted) may be hyponyms) · graph-theoretical (some (unsorted) may be hyponyms) · graphiology (some (unsorted) may be hyponyms) · cocktail party graph (some (unsorted) may be hyponyms) · Coxeter graph (some (unsorted) may be hyponyms) · factor graph (some (unsorted) may be hyponyms) · complete bipartite graph (some (unsorted) may be hyponyms) · dual graph (some (unsorted) may be hyponyms) · elastograph (some (unsorted) may be hyponyms) · flowgraph (some (unsorted) may be hyponyms) · plane graph (some (unsorted) may be hyponyms) · regraph (some (unsorted) may be hyponyms) · brain graph (some (unsorted) may be hyponyms) · graphon (some (unsorted) may be hyponyms) · Turán graph (some (unsorted) may be hyponyms) · gastrograph (some (unsorted) may be hyponyms) · metagraph (some (unsorted) may be hyponyms) · cograph (some (unsorted) may be hyponyms) · integraph (some (unsorted) may be hyponyms) · braingraph (some (unsorted) may be hyponyms) · graphophone (some (unsorted) may be hyponyms) · directed acyclic graph (some (unsorted) may be hyponyms) · graph thickness (some (unsorted) may be hyponyms) · call graph (some (unsorted) may be hyponyms) · Cayley graph (some (unsorted) may be hyponyms) · cherry graph (some (unsorted) may be hyponyms) · conceptual graph (some (unsorted) may be hyponyms) · graphic matroid (some (unsorted) may be hyponyms) · hypergraph (some (unsorted) may be hyponyms) · graph geodesic (some (unsorted) may be hyponyms) · supergraph (some (unsorted) may be hyponyms) · Tanner graph (some (unsorted) may be hyponyms) · knowledge graph (some (unsorted) may be hyponyms) · ergograph (some (unsorted) may be hyponyms) · graph eccentricity (some (unsorted) may be hyponyms) · graph paper (some (unsorted) may be hyponyms) · graph centre (some (unsorted) may be hyponyms) · topological graph (some (unsorted) may be hyponyms) · graph homomorphism (some (unsorted) may be hyponyms) · graph polynomial (some (unsorted) may be hyponyms) · graphlet (some (unsorted) may be hyponyms) · medial graph (some (unsorted) may be hyponyms) · spider graph (some (unsorted) may be hyponyms) · telegraph (some (unsorted) may be hyponyms) · directed acyclic word graph (some (unsorted) may be hyponyms) · streamgraph (some (unsorted) may be hyponyms) · Moore graph (some (unsorted) may be hyponyms) · bigraph (some (unsorted) may be hyponyms) · planar graph (some (unsorted) may be hyponyms) · graph theorist (some (unsorted) may be hyponyms) · rectagraph (some (unsorted) may be hyponyms) · fatgraph (some (unsorted) may be hyponyms) · sonograph (some (unsorted) may be hyponyms) · Herschel graph (some (unsorted) may be hyponyms) · graph-theoretic (some (unsorted) may be hyponyms) · de Bruijn graph (some (unsorted) may be hyponyms) · termgraph (some (unsorted) may be hyponyms) · empty graph (some (unsorted) may be hyponyms) · stream graph (some (unsorted) may be hyponyms) · utility graph (some (unsorted) may be hyponyms) · phenograph (some (unsorted) may be hyponyms) · block graph (some (unsorted) may be hyponyms) · graph minor (some (unsorted) may be hyponyms) · graph state (some (unsorted) may be hyponyms) · graph topology (some (unsorted) may be hyponyms) · scenegraph (some (unsorted) may be hyponyms) · graph directrix (some (unsorted) may be hyponyms) · algebraic graph theory (some (unsorted) may be hyponyms) · Laves graph (some (unsorted) may be hyponyms) · hypograph (some (unsorted) may be hyponyms) · Levi graph (some (unsorted) may be hyponyms) · spirograph (some (unsorted) may be hyponyms) · graphoid (some (unsorted) may be hyponyms) · karyograph (some (unsorted) may be hyponyms) · graph spectrum (some (unsorted) may be hyponyms) · graph antihole (some (unsorted) may be hyponyms) · viewgraph (some (unsorted) may be hyponyms) · graph eigenvalue (some (unsorted) may be hyponyms) · graph-theoretically (some (unsorted) may be hyponyms) · Desargues graph (some (unsorted) may be hyponyms) · fluviograph (some (unsorted) may be hyponyms) · graph hole (some (unsorted) may be hyponyms) · logograph (some (unsorted) may be hyponyms) · graphable (some (unsorted) may be hyponyms) · graphlike (some (unsorted) may be hyponyms) · crown graph (some (unsorted) may be hyponyms)
Hyponyms
multigraph (Derived terms for types of graph) · voltage graph (Derived terms for types of graph) · biased graph (Derived terms for types of graph) · Thomsen graph (Derived terms for types of graph) · subgraph (Derived terms for types of graph) · strongly regular graph (Derived terms for types of graph) · dependency graph (Derived terms for types of graph) · line graph (Derived terms for types of graph) · small world graph (Derived terms for types of graph) · superregular graph (Derived terms for types of graph) · Ramanujan graph (Derived terms for types of graph) · windmill graph (Derived terms for types of graph) · flame graph (Derived terms for types of graph) · complete graph (Derived terms for types of graph) · Heawood graph (Derived terms for types of graph) · Yao graph (Derived terms for types of graph) · regular graph (Derived terms for types of graph) · polygon-circle graph (Derived terms for types of graph) · Kneser graph (Derived terms for types of graph) · tree · Hamiltonian graph (Derived terms for types of graph) · Mycielski graph (Derived terms for types of graph) · acyclic graph (Derived terms for types of graph) · control-flow graph (Derived terms for types of graph) · forest · diamond graph (Derived terms for types of graph) · unicursal graph (Derived terms for types of graph) · scene graph (Derived terms for types of graph) · weighted graph (Derived terms for types of graph) · circular graph (Derived terms for types of graph) · bipartite graph (Derived terms for types of graph) · Meyniel graph (Derived terms for types of graph) · functional graph (Derived terms for types of graph) · Petersen graph (Derived terms for types of graph) · pseudograph (Derived terms for types of graph) · random graph (Derived terms for types of graph) · digraph (Derived terms for types of graph) · clique · object graph (Derived terms for types of graph) · oriented graph (Derived terms for types of graph) · theta graph (Derived terms for types of graph) · Eulerian graph (Derived terms for types of graph) · connected graph (Derived terms for types of graph) · Grötzsch graph (Derived terms for types of graph) · biconnected graph (Derived terms for types of graph) · undirected graph (Derived terms for types of graph) · nonoriented graph (Derived terms for types of graph) · Keller graph (Derived terms for types of graph) · directed graph (Derived terms for types of graph) · signed graph (Derived terms for types of graph)
Meronyms
edge · node · subgraph · vertex · route · path · cycle · connected component
Relateds
graphical · graphism · Appendix:Glossary of graph theory · grapheme · graphic
Synonyms
graph · topological graph · glyph
Translations (118)
kk график (graph of a function) · de Funktionsgraph (graph of a function) · cy graff (graph of a function) · ru граф (set of vertices connected by edges) · az qrafik (graph of a function) · ar مُخَطَّط بَيَانِيّ (graph of a function) · uk діагра́ма (graph of a function) · sh grȁf (graph of a function) · sv diagram (graph of a function) · bg гра́фика (graph of a function) · mn ᠭᠷᠠᠹᠢᠻ (graph of a function) · it grafo (set of vertices connected by edges) · he גְּרָף (graph of a function) · nl grafiek (graph of a function) · ky график (graph of a function) · ga graf (graph of a function) · vi biểu đồ (set of vertices connected by edges) · es gráfico (graph of a function) · lv grafs (graph of a function) · ko 도표 (set of vertices connected by edges) · bg граф (set of vertices connected by edges) · lv grafiks (graph of a function) · hi लेखाचित्र (graph of a function) · ur گراف (graph of a function) · th กราฟ (graph of a function) · cs graf (set of vertices connected by edges) · sv graf (graph of a function) · sk graf (graph of a function) · es grafo (set of vertices connected by edges) · th กราฟ (set of vertices connected by edges) · fi graafi (set of vertices connected by edges) · fa نمودار (graph of a function) · ms graf (graph of a function) · sv graf (set of vertices connected by edges) · sh гра̏ф (set of vertices connected by edges) · hu gráf (set of vertices connected by edges) · sk graf (set of vertices connected by edges) · de Graph (set of vertices connected by edges) · sh grȁf (set of vertices connected by edges) · ko 도표 (graph of a function) · ja 図表 (set of vertices connected by edges) · lo ກຣາຟ (graph of a function) · sw jedwali (graph of a function) · de Graph (graph of a function) · he גְּרָף (set of vertices connected by edges) · ru гра́фик (graph of a function) · ca gràfic (graph of a function) · nb graf (graph of a function) · hi लेखाचित्र (set of vertices connected by edges) · sq grafik (graph of a function) · gl gráfico (graph of a function) · gd graf (graph of a function) · pl graf (set of vertices connected by edges) · hu ábra (graph of a function) · tr grafik (graph of a function) · ja グラフ (set of vertices connected by edges) · ru диагра́мма (graph of a function) · fi verkko (set of vertices connected by edges) · ca graf (set of vertices connected by edges) · lt grafikas (graph of a function) · uk граф (set of vertices connected by edges) · uz grafik (graph of a function) · tk grafik (graph of a function) · mk графико́н (graph of a function) · fr graphique (graph of a function) · hu grafikon (graph of a function) · cmn 圖表 /图表 (graph of a function) · ro grafic (graph of a function) · ja 図表 (graph of a function) · ko 그래프 (graph of a function) · bg диагра́ма (graph of a function) · tg график (graph of a function) · pt grafo (set of vertices connected by edges) · hy գրաֆիկ (graph of a function) · id grafik (graph of a function) · es gráfica (chart) · eo grafeo (graph of a function) · da graf (graph of a function) · es gráfico (chart) · mi kauwhata (graph of a function) · my ဂရပ် (graph of a function) · lo ເສັ້ນສະແດງ (graph of a function) · sl graf (graph of a function) · el γράφημα (set of vertices connected by edges) · tl talangguhit (graph of a function) · mn график (graph of a function) · hi ग्राफ़ (graph of a function) · ro graf (set of vertices connected by edges) · cmn 圖表 /图表 (set of vertices connected by edges) · fi diagrammi (graph of a function) · ko 그래프 (set of vertices connected by edges) · da graf (set of vertices connected by edges) · bn গ্রাফ (graph of a function) · fa گراف (graph of a function) · uk гра́фік (graph of a function) · be граф (set of vertices connected by edges) · cmn 圖 /图 (set of vertices connected by edges) · cs graf (graph of a function) · ga graf (set of vertices connected by edges) · fi kaaviokuva (graph of a function) · ast gráficu (graph of a function) · pl wykres (graph of a function) · vi biểu đồ (graph of a function) · sh гра̏ф (graph of a function) · fr graphe (set of vertices connected by edges) · be гра́фік (graph of a function) · pt gráfico (graph of a function) · et graafik (graph of a function) · ka გრაფიკი (graph of a function) · nl graaf (set of vertices connected by edges) · it grafico (graph of a function) · af grafiek (graph of a function) · km ពិន្ទុរេខីយ (graph of a function) · el γράφος (set of vertices connected by edges) · lt grafas (graph of a function) · be дыягра́ма (graph of a function) · el γράφημα (graph of a function) · ja グラフ (graph of a function)