# graph

Pronunciation: US say "GRAF" /ɡɹæf/; UK say "GRAHF" /ɡɹɑːf/

## Noun

1. A chart that shows how one or more sets of numbers, such as quantities or measurements, relate to a reference set whose members may or may not be numbers.
   - Simple: A drawing that shows how a set of numbers relates to another set of things.
   - _The graph of monthly sales showed a sharp dip every February._
   - _The report's graphs compare unemployment rates across twelve countries._
2. In mathematics, a set of points, called vertices or nodes, together with links, called edges, that join pairs of them.
   - Simple: In math, a group of points, some of them joined to each other by lines.
   - _In a complete graph, every vertex is joined by an edge to every other vertex._
   - _Mapping software treats the road network as a graph and searches it for the shortest route between two vertices._
4. In mathematics, the set of points representing a real function: every combination of inputs paired with the value the function gives them.
   - Simple: In math, all the points that show a function, with each input matched to its output.
   - _The graph of the sine function rises and falls in a repeating wave._
   - _A smooth function of two variables has a graph that forms a surface in three-dimensional space._

## Verb

3. To represent something, such as a set of data or a mathematical function, in the form of a graph.
   - Simple: To show something, like a set of numbers, by drawing a graph of it.
   - _Students graph the equation y = 2x + 1 and mark where the line crosses the y-axis._
   - _Rainfall was graphed against crop yield for each of the past twenty years._

## Other meanings

- (noun) In topology, a space built from vertices and edges by making each vertex a point and each edge a copy of the interval [0, 1] between its two vertices, with the graph topology.
- (noun) In category theory, the morphism from the domain of a morphism f into the product of its domain and codomain whose projections give the identity and f respectively.
- (noun) The basic written shape of a letter or character, apart from any one typeface or hand that draws it; unlike a grapheme, it does not by itself distinguish meaning.

## Origin

Graph began as a shortened form of graphic formula and is recorded from 1878. The verb came later, in 1889.

Source: DictionaryAI, https://dictionaryai.com/define/graph (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).