graph
EnglishEdit
EtymologyEdit
Shortening of graphic formula. From 1878; verb from 1889.^{[1]}
PronunciationEdit
 (Received Pronunciation) IPA^{(key)}: /ɡɹɑːf/
 (US, Northern England) IPA^{(key)}: /ɡɹæf/
Audio (US) (file)  Rhymes: ɑːf, æf
NounEdit
graph (plural graphs)
 (applied mathematics, statistics) 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.
 Hyponyms: bar graph, line graph, pie graph
 2012 March 1, Brian Hayes, “Pixels or Perish”, in American Scientist^{[1]}, volume 100, number 2, page 106:
 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.
 (mathematics) A set of points constituting a graphical representation of a real function; (formally) a set of tuples , where for a given function .
 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, , that is, the point .
 1969 [MIT Press], Thomas Walsh, Randell Magee (translators), I. M. Gelfand, E. G. Glagoleva, E. E. Shnol, Functions and Graphs, 2002, Dover, page 19,
 (graph theory) (formally) An ordered pair of sets , where the elements of are called vertices or nodes and is a set of pairs (called edges) of elements of ; (less formally) a set of vertices (or nodes) together with a set of edges that connect (some of) the vertices.
 Hyponyms: directed graph, undirected graph, tree
 1973, Edward Minieka (translator), Claude Berge, Graphs and Hypergraphs, Elsevier (NorthHolland), [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.
 1997, Fan R. K. Chung, Spectral Graph Theory, American Mathematical Society, page 1,
 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.
 (topology) 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.
 Synonym: topological graph
 2008, Unnamed translators (AMS), A. V. Alexeevski, S. M. Natanzon, Hurwitz Numbers for Regular Coverings of Surfaces by Seamed Surfaces and CardyFrobenius Algebras of Finite Groups, V. M. Buchstaber, I. M. Krichever (editors), Geometry, Topology, and Mathematical Physics: S.P. Novikov's Seminar, 20062007, American Mathematical Society, page 6,
 First, let us define its 1dimensional analog, that is, a topological graph. A graph is a 1dimensional stratified topological space with finitely many 0strata (vertices) and finitely many 1strata (edges). […] A graph such that any vertex belongs to at least two halfedges we call an sgraph. Clearly the boundary of a surface with marked points is an sgraph.
 A morphism of graphs is a continuous epimorphic map of graphs compatible with the stratification; i.e., the restriction of to any open 1stratum (interior of an edge) of is a local (therefore, global) homeomorphism with appropriate open 1stratum of .
 (category theory, of a morphism f) A morphism from the domain of to the product of the domain and codomain of , such that the first projection applied to equals the identity of the domain, and the second projection applied to is equal to .
 (linguistics, typography) A graphical unit on the tokenlevel, the abstracted fundamental shape of a character or letter as distinct from its ductus (realization in a particular typeface or handwriting on the instancelevel) and as distinct by a grapheme on the typelevel by not fundamentally distinguishing meaning.
 Synonym: glyph
 2003, J. Richard Andrews, Introduction to Classical Nahuatl, Revised Edition, University of Oklahoma Press, page 10:
 A graph is a tokenlevel 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 notesEdit
 In mathematics, the graphical representation of a function sense is generally of interest only at an elementary level.
 Nevertheless, the term vertexedge graph is 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).
 The function is a set of ordered pairs , where is a point in and is a point in .
 A graph of is a set of points (represented as ntuples) .
 A graph is similar to, but not the same as a (real) function (as defined formally).
 (graph theory):
 A graph may be defined such that the elements of are ordered pairs or unordered pairs.
 If the pairs are unordered, may be called an undirected graph and the elements of are called edges.
 If the pairs are ordered, is called a directed graph or digraph and the elements of may be called arcs; the notation is sometimes used.
 If the two vertices of an edge represent the same point, the edge may be called a loop.
 A graph may be defined such that the elements of are ordered pairs or unordered pairs.
HyponymsEdit
Derived terms for types of graph
 acyclic graph
 biased graph
 biconnected graph
 bipartite graph
 complete graph
 connected graph
 dependency graph
 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
 unicursal graph
 voltage graph
 weighted graph
Derived termsEdit
Related termsEdit
TranslationsEdit
chart — see chart
mathematical diagram


ordered pair in graph theory


VerbEdit
graph (thirdperson singular simple present graphs, present participle graphing, simple past and past participle graphed)
 (transitive) To draw a graph.
 (transitive, mathematics) To draw a graph of a function.
SynonymsEdit
TranslationsEdit
draw a graph of


See alsoEdit
ReferencesEdit
Further readingEdit
 Chart on Wikipedia.Wikipedia
 Graph of a function on Wikipedia.Wikipedia
 Graph theory on Wikipedia.Wikipedia
 Graph (discrete mathematics) on Wikipedia.Wikipedia
 Graph (topology) on Wikipedia.Wikipedia
 Graph (abstract data type) on Wikipedia.Wikipedia
 Conceptual graph on Wikipedia.Wikipedia
 Glyph (disambiguation) on Wikipedia.Wikipedia
 Tree (disambiguation) on Wikipedia.Wikipedia
 Graph on Encyclopedia of Mathematics
 graph on nLab
 graph of a function on nLab
 graph of a functor on nLab
 Graph on Wolfram MathWorld