Definition of "graph"

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, Brian Hayes, “Pixels or Perish”, in American Scientist‎, volume 100, number 2, archived from the original on 19 February 2013, page 106

Let us take any point of the first graph, for example, x = 1 2 , y = 4 5 {\displaystyle \textstyle x={\frac {1}{2}},y={\frac {4}{5}}} , that is, the point M 1 ( 1 2 , 4 5 ) {\displaystyle \textstyle M_{1}({\frac {1}{2}},{\frac {4}{5}})} .

1969 [MIT Press], Thomas Walsh, Randell Magee (translators), I. M. Gelfand, E. G. Glagoleva, E. E. Shnol, Functions and Graphs, 2002, Dover, page 19

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.

1973, Edward Minieka (translator), Claude Berge, Graphs and Hypergraphs, Elsevier (North-Holland), page vii

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

First, let us define its 1-dimensional analog, that is, a topological graph. A graph Δ {\displaystyle \Delta } 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 {\displaystyle \partial \Omega } of a surface Ω {\displaystyle \Omega } with marked points is an s-graph. / A morphism of graphs φ : Δ ′ → Δ ″ {\displaystyle \varphi :\Delta '\rightarrow \Delta ''} is a continuous epimorphic map of graphs compatible with the stratification; i.e., the restriction of φ {\displaystyle \varphi } to any open 1-stratum (interior of an edge) of Δ ′ {\displaystyle \Delta '} is a local (therefore, global) homeomorphism with appropriate open 1-stratum of Δ ″ {\displaystyle \Delta ''} .

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

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