graph

Pluralgraphs

Formsgraphs, graphing, graphed

1. 1
   diagram (data)nouncountable

   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.

   The graph of monthly sales showed a sharp dip every February.

   The report's graphs compare unemployment rates across twelve countries.

   UsageUsually a graph of something (a graph of sales), with the points or lines on the graph.

   Similarchart, plot, diagram

   Note

   In a typical graph the reference set, often time or a list of categories, runs along the horizontal axis and the measured numbers along the vertical one. A line graph joins its points to show change; a bar graph suits separate categories such as countries or products. The noun began in 1878 as a clipping of graphic formula, a chemist's diagram of linked atoms; the chart meaning came later, and the verb in 1889. Source

   Checked 3 Nov 2026 · 4 facts

   • The noun dates from 1878 and is a clipping of graphic formula. en.wiktionary.org
   • A chemical graphic formula depicts linked atoms. en.wikipedia.org
   • The plotted-curve meaning developed after the 1878 chemical-diagram meaning. mathshistory.st-andrews.ac.uk
   • The verb dates from 1889. en.wiktionary.org
2. 2
   network (math)nouncountable

   In mathematics, a set of points, called vertices or nodes, together with links, called edges, that join pairs of them.

   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.

   Note

   Only the links count here, not where the vertices sit, so one graph can be drawn in many shapes and none is more correct than another. Nothing is plotted against axes, which sets it apart from the chart of data. Edges may carry directions or weights, giving directed and weighted graphs, which model road maps, computer networks and friendships. Source

   Checked 3 Nov 2026 · 3 facts

   • A graph's connectivity is independent of the positions used to draw its vertices. en.wikipedia.org
   • A graph in this mathematical sense is distinct from a plot against numerical axes. math.libretexts.org
   • Edges can have directions or weights. math.libretexts.org
3. 3
   draw a chartverbtransitive

   To represent something, such as a set of data or a mathematical function, in the form of a graph.

   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.

   UsageOne quantity is often graphed against another, or over time.

   Similarplot, chart

4. 4
   function (math)nouncountable

   In mathematics, the set of points representing a real function: every combination of inputs paired with the value the function gives them.

   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.

   Note

   Mathematicians mean the set of points itself, not a drawing of it: for a function of one variable it is every pair (x, f(x)) in the plane, and a sketch often shows only part of it. That is why the vertical line test works. No input can appear with two outputs, so a vertical line meets the graph of a function at most once. Source

   Checked 3 Nov 2026 · 3 facts

   • The graph of a real function of one variable is the set of pairs (x, f(x)) in the plane. openstax.org
   • A sketch may show the whole graph. For example, the source's function with domain {1,2,3,4,5} has just five graph points; plotting all five gives a counterexample. openstax.org
   • A function assigns only one output to each input, which explains why every vertical line intersects its graph at most once. openstax.org

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