graph

noun

1. 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.”

2. 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).”

3. 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.”

4. 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.
5. 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.
6. 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.”

verb

1. (transitive)To draw a graph, to record graphically.

   “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.”

2. (transitive)To draw a graph of a function.