4.1 Graphs

The graph of an equation may formally be defined as the set of points which satisfy that equation. Given a specification   the graph of S is defined as follows:  

For example,

The formalism alone does not fully communicate the true nature of graphs: the visual nature of geometry must be reconciled with the dry, algebraic character of the formalism presented to fully capture the true nature of graphs. Mathematicians often refer to graphs as relations [65]. This is clear, as the formal definition of a graph is identical in graph theory [41] and geometry, but the two concepts are commonly thought of as distinct.

Jeff Tupper

March 1996