graph
Language: English
Part of speech: noun
Pronunciation: ipa: /ɡɹɑːf/
ipa: /ɡɹæf/
rhymes: -ɑːf
rhymes: -æf
Forms: form: graphs
Etymology: Clipping of graphic formula. From 1878; verb from 1889.
Senses: examples: text: 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.
ref: 2012 March 23, Brian Hayes, “Pixels or Perish”, in American Scientist, volume 100, number 2, archived from the original on 19 Feb 2013, page 106:
topics: mathematics
sciences
statistics
qualifier: applied mathematics
glosses: 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.
examples: 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).
topics: mathematics
sciences
glosses: 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
examples: text: 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.
text: 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.
ref: 1997, Fan R. K. Chung, Spectral Graph Theory, American Mathematical Society, page 1:
topics: graph-theory
mathematics
sciences
glosses: 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
examples: 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.
topics: mathematics
sciences
topology
synonyms: topological graph
glosses: 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.
topics: category-theory
computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
glosses: 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.
raw_tags: of a morphism f
examples: text: 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.
ref: 2003, J. Richard Andrews, Introduction to Classical Nahuatl, Revised Edition, University of Oklahoma Press, page 10:
topics: human-sciences
linguistics
media
publishing
sciences
typography
synonyms: glyph
glosses: 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.
Synonyms: word: graph
Hyponyms: sense: Derived terms for types of graph
word: acyclic graph
sense: Derived terms for types of graph
word: biased graph
sense: Derived terms for types of graph
word: biconnected graph
sense: Derived terms for types of graph
word: bipartite graph
sense: Derived terms for types of graph
word: circular graph
sense: Derived terms for types of graph
word: complete graph
sense: Derived terms for types of graph
word: connected graph
sense: Derived terms for types of graph
word: control-flow graph
sense: Derived terms for types of graph
word: dependency graph
sense: Derived terms for types of graph
word: diamond graph
sense: Derived terms for types of graph
word: digraph
sense: Derived terms for types of graph
word: directed graph
sense: Derived terms for types of graph
word: Eulerian graph
sense: Derived terms for types of graph
word: flame graph
sense: Derived terms for types of graph
word: functional graph
sense: Derived terms for types of graph
word: Grötzsch graph
sense: Derived terms for types of graph
word: Hamiltonian graph
sense: Derived terms for types of graph
word: Heawood graph
sense: Derived terms for types of graph
word: Keller graph
sense: Derived terms for types of graph
word: Kneser graph
sense: Derived terms for types of graph
word: line graph
sense: Derived terms for types of graph
word: Meyniel graph
sense: Derived terms for types of graph
word: multigraph
sense: Derived terms for types of graph
word: Mycielski graph
sense: Derived terms for types of graph
word: nonoriented graph
sense: Derived terms for types of graph
word: object graph
sense: Derived terms for types of graph
word: oriented graph
sense: Derived terms for types of graph
word: Petersen graph
sense: Derived terms for types of graph
word: polygon-circle graph
sense: Derived terms for types of graph
word: pseudograph
sense: Derived terms for types of graph
word: Ramanujan graph
sense: Derived terms for types of graph
word: random graph
sense: Derived terms for types of graph
word: regular graph
sense: Derived terms for types of graph
word: scene graph
sense: Derived terms for types of graph
word: signed graph
sense: Derived terms for types of graph
word: small world graph
sense: Derived terms for types of graph
word: strongly regular graph
sense: Derived terms for types of graph
word: subgraph
sense: Derived terms for types of graph
word: superregular graph
sense: Derived terms for types of graph
word: theta graph
sense: Derived terms for types of graph
word: undirected graph
sense: Derived terms for types of graph
word: unicursal graph
sense: Derived terms for types of graph
word: voltage graph
sense: Derived terms for types of graph
word: weighted graph
sense: Derived terms for types of graph
word: windmill graph
sense: Derived terms for types of graph
word: Yao graph
word: tree
word: forest
word: clique
Meronyms: word: node
word: vertex
word: edge
word: cycle
word: path
word: route
word: connected component
word: subgraph
Derived terms: sense: some (unsorted) may be hyponyms
word: algebraic graph theory
sense: some (unsorted) may be hyponyms
word: bigraph
sense: some (unsorted) may be hyponyms
word: block graph
sense: some (unsorted) may be hyponyms
word: braingraph
sense: some (unsorted) may be hyponyms
word: brain graph
sense: some (unsorted) may be hyponyms
word: bullet graph
sense: some (unsorted) may be hyponyms
word: call graph
sense: some (unsorted) may be hyponyms
word: Cayley graph
sense: some (unsorted) may be hyponyms
word: cherry graph
sense: some (unsorted) may be hyponyms
word: cocktail party graph
sense: some (unsorted) may be hyponyms
word: cograph
sense: some (unsorted) may be hyponyms
word: complete bipartite graph
sense: some (unsorted) may be hyponyms
word: conceptual graph
sense: some (unsorted) may be hyponyms
word: Coxeter graph
sense: some (unsorted) may be hyponyms
word: crown graph
sense: some (unsorted) may be hyponyms
word: cubic graph
sense: some (unsorted) may be hyponyms
word: de Bruijn graph
sense: some (unsorted) may be hyponyms
word: Desargues graph
sense: some (unsorted) may be hyponyms
word: directed acyclic graph
sense: some (unsorted) may be hyponyms
word: directed acyclic word graph
sense: some (unsorted) may be hyponyms
word: dual graph
sense: some (unsorted) may be hyponyms
word: elastograph
sense: some (unsorted) may be hyponyms
word: empty graph
sense: some (unsorted) may be hyponyms
word: ergograph
sense: some (unsorted) may be hyponyms
word: factor graph
sense: some (unsorted) may be hyponyms
word: fatgraph
sense: some (unsorted) may be hyponyms
word: flowgraph
sense: some (unsorted) may be hyponyms
word: fluviograph
sense: some (unsorted) may be hyponyms
word: gastrograph
sense: some (unsorted) may be hyponyms
word: graphable
sense: some (unsorted) may be hyponyms
word: graph antihole
sense: some (unsorted) may be hyponyms
word: graph centre
sense: some (unsorted) may be hyponyms
word: graph directrix
sense: some (unsorted) may be hyponyms
word: graph eccentricity
sense: some (unsorted) may be hyponyms
word: graph eigenvalue
sense: some (unsorted) may be hyponyms
word: graph geodesic
sense: some (unsorted) may be hyponyms
word: graph hole
sense: some (unsorted) may be hyponyms
word: graph homomorphism
sense: some (unsorted) may be hyponyms
word: graphic matroid
sense: some (unsorted) may be hyponyms
word: graphiology
sense: some (unsorted) may be hyponyms
word: graphlet
sense: some (unsorted) may be hyponyms
word: graphlike
sense: some (unsorted) may be hyponyms
word: graph minor
sense: some (unsorted) may be hyponyms
word: graphoid
sense: some (unsorted) may be hyponyms
word: graphon
sense: some (unsorted) may be hyponyms
word: graphophone
sense: some (unsorted) may be hyponyms
word: graph paper
sense: some (unsorted) may be hyponyms
word: graph polynomial
sense: some (unsorted) may be hyponyms
word: graph spectrum
sense: some (unsorted) may be hyponyms
word: graph state
sense: some (unsorted) may be hyponyms
word: graph-theoretic
sense: some (unsorted) may be hyponyms
word: graph-theoretical
sense: some (unsorted) may be hyponyms
word: graph-theoretically
sense: some (unsorted) may be hyponyms
word: graph theorist
sense: some (unsorted) may be hyponyms
word: graph thickness
sense: some (unsorted) may be hyponyms
word: graph topology
sense: some (unsorted) may be hyponyms
word: graph toughness
sense: some (unsorted) may be hyponyms
word: graphwork
sense: some (unsorted) may be hyponyms
word: Herschel graph
sense: some (unsorted) may be hyponyms
word: hypergraph
sense: some (unsorted) may be hyponyms
word: hypograph
sense: some (unsorted) may be hyponyms
word: integraph
sense: some (unsorted) may be hyponyms
word: karyograph
sense: some (unsorted) may be hyponyms
word: knowledge graph
sense: some (unsorted) may be hyponyms
word: Laves graph
sense: some (unsorted) may be hyponyms
word: Levi graph
sense: some (unsorted) may be hyponyms
word: logograph
sense: some (unsorted) may be hyponyms
word: medial graph
sense: some (unsorted) may be hyponyms
word: metagraph
sense: some (unsorted) may be hyponyms
word: Moore graph
sense: some (unsorted) may be hyponyms
word: phenograph
sense: some (unsorted) may be hyponyms
word: planar graph
sense: some (unsorted) may be hyponyms
word: plane graph
sense: some (unsorted) may be hyponyms
word: protograph
sense: some (unsorted) may be hyponyms
word: rectagraph
sense: some (unsorted) may be hyponyms
word: regraph
sense: some (unsorted) may be hyponyms
word: scenegraph
sense: some (unsorted) may be hyponyms
word: social graph
sense: some (unsorted) may be hyponyms
word: sonograph
sense: some (unsorted) may be hyponyms
word: spider graph
sense: some (unsorted) may be hyponyms
word: spirograph
sense: some (unsorted) may be hyponyms
word: stream graph
sense: some (unsorted) may be hyponyms
word: streamgraph
sense: some (unsorted) may be hyponyms
word: supergraph
sense: some (unsorted) may be hyponyms
word: Tanner graph
sense: some (unsorted) may be hyponyms
word: telegraph
sense: some (unsorted) may be hyponyms
word: termgraph
sense: some (unsorted) may be hyponyms
word: topological graph
sense: some (unsorted) may be hyponyms
word: Turán graph
sense: some (unsorted) may be hyponyms
word: ultragraph
sense: some (unsorted) may be hyponyms
word: utility graph
sense: some (unsorted) may be hyponyms
word: viewgraph
Related terms: word: grapheme
word: graphic
word: graphical
word: graphism
word: Appendix:Glossary of graph theory