graph
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[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Demography_graphic_of_Pichilemu.png/220px-Demography_graphic_of_Pichilemu.png)
Etymology
[edit]Clippingofgraphicformula.From 1878; verb from 1889.[1]
Pronunciation
[edit]- (Received Pronunciation)IPA(key):/ɡɹɑːf/
- (US,Northern England)IPA(key):/ɡɹæf/
Audio(US): (file) - Rhymes:-ɑːf,-æf
Noun
[edit]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,wherefor a given function.See also
Graph 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,,that is, the point.
- 1969[MIT Press], Thomas Walsh, Randell Magee (translators), I. M. Gelfand, E. G. Glagoleva, E. E. Shnol,Functions andGraphs,2002, Dover,page 19,
- (graph theory)A set ofvertices(ornodes) connected together byedges;(formally)anordered pairof sets,where theelementsofare calledverticesornodesandis a set of pairs (callededges) of elements of.See also
Graph (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. Agraphis 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 boundaryof a surfacewith marked points is an s-graph.
- A morphism ofgraphsis a continuous epimorphic map ofgraphscompatible with the stratification; i.e., the restriction ofto any open 1-stratum (interior of an edge) ofis a local (therefore, global) homeomorphism with appropriate open 1-stratum of.
- (category theory,of a morphism f)Amorphismfrom thedomainofto theproductof the domain andcodomainof,such that the first projection applied toequals theidentityof the domain, and the second projection applied tois equal to.
- (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
[edit]- 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).
- Thefunctionis a set ofordered pairs,whereis a point inandis a point in.
- Agraphofis a set ofpoints(represented asn-tuples).
- A graph is similar to, but not the same as a (real) function (as defined formally).
- (graph theory):
- A graphmay be defined such that the elements ofareordered pairsorunorderedpairs.
- If the pairs are unordered,may be called anundirected graphand the elements ofare callededges.
- If the pairs are ordered,is called adirected graphordigraphand the elements ofmay be calledarcs;the notationis sometimes used.
- If the two vertices of an edge represent the same point, the edge may be called aloop.
- A graphmay be defined such that the elements ofareordered pairsorunorderedpairs.
Hyponyms
[edit]Derived terms for types of graph
- acyclic graph
- biased graph
- biconnected graph
- bipartite graph
- complete graph
- connected graph
- dependency graph
- directed graph
- Eulerian graph
- flame graph
- Hamiltonian graph
- Heawood graph
- Keller graph
- line graph
- multigraph
- nonoriented graph
- object graph
- oriented graph
- Petersen graph
- polygon-circle graph
- pseudograph
- Ramanujan graph
- random graph
- regular graph
- signed graph
- small world graph
- strongly regular graph
- subgraph
- superregular graph
- undirected graph
- unicursal graph
- voltage graph
- weighted graph
- See also
Graph (discrete mathematics)on Wikipedia.Wikipedia
- See alsoThesaurus:graph
Derived terms
[edit]some (unsorted) may be hyponyms
- algebraic graph theory
- bigraph
- block graph
- braingraph
- brain graph
- bullet graph
- call graph
- Cayley graph
- cherry graph
- cocktail party graph
- cograph
- complete bipartite graph
- conceptual graph
- Coxeter graph
- crown graph
- cubic graph
- de Bruijn graph
- Desargues graph
- directed acyclic graph
- directed acyclic word graph
- dual graph
- elastograph
- empty graph
- ergograph
- factor graph
- fatgraph
- flowgraph
- fluviograph
- gastrograph
- graphable
- graph antihole
- graph centre
- graph eccentricity
- graph eigenvalue
- graph geodesic
- graph hole
- graphic matroid
- graphiology
- graphlet
- graphlike
- graph minor
- graphoid
- graphon
- graphophone
- graph paper
- graph polynomial
- graph spectrum
- graph state
- graph-theoretic
- graph-theoretical
- graph-theoretically
- graph theorist
- graph thickness
- graph topology
- graph toughness
- graphwork
- Herschel graph
- hypergraph
- hypograph
- integraph
- karyograph
- knowledge graph
- Laves graph
- Levi graph
- logograph
- medial graph
- metagraph
- Moore graph
- phenograph
- planar graph
- plane graph
- protograph
- rectagraph
- regraph
- scenegraph
- social graph
- sonograph
- spider graph
- spirograph
- stream graph
- streamgraph
- supergraph
- Tanner graph
- telegraph
- termgraph
- topological graph
- Turán graph
- ultragraph
- utility graph
- viewgraph
Related terms
[edit]Translations
[edit]chart—seechart
graph of a function
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set of vertices connected by edges
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Verb
[edit]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
[edit]Translations
[edit]draw a graph of
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See also
[edit]References
[edit]- ^Douglas Harper (2001–2024) “graph”,inOnline Etymology Dictionary.
Further reading
[edit]Charton Wikipedia.Wikipedia
Graph of a functionon Wikipedia.Wikipedia
Graph theoryon Wikipedia.Wikipedia
Graph (discrete mathematics)on Wikipedia.Wikipedia
Graph (topology)on Wikipedia.Wikipedia
Graph (abstract data type)on Wikipedia.Wikipedia
Conceptual graphon Wikipedia.Wikipedia
Glyph (disambiguation)on Wikipedia.Wikipedia
Tree (disambiguation)on Wikipedia.Wikipedia
- GraphonEncyclopedia of Mathematics
- graphonnLab
- graph of a functiononnLab
- graph of a functoronnLab
- GraphonWolfram MathWorld
Anagrams
[edit]Categories:
- English terms derived from Proto-Indo-European
- English terms derived from the Proto-Indo-European root *gerbʰ-
- English clippings
- English 1-syllable words
- English terms with IPA pronunciation
- English terms with audio links
- Rhymes:English/ɑːf
- Rhymes:English/ɑːf/1 syllable
- Rhymes:English/æf
- Rhymes:English/æf/1 syllable
- English lemmas
- English nouns
- English countable nouns
- en:Statistics
- English terms with quotations
- en:Mathematics
- en:Curves
- en:Functions
- en:Graph theory
- en:Topology
- en:Category theory
- en:Linguistics
- en:Typography
- English verbs
- English transitive verbs
- en:Visualization