There are two types of graph that exist in mathematics.
The first form is the one with which most people are familiar with; a representation of a relationship between variables (often x and y) expressed as a line or curve (as in figure 1). An example of the second form of graph is shown in figure 2. This second form represents relationships that are found in discrete mathematics. In discrete mathematics the set of elements is countable and has a one-to-one correspondence with either the set of positive integers, or a subset of the positive integers.
Figure 1: a plot of the function y = (x – 2)² + 1. A function graph as found in continuous mathematics.
Figure 2: a graph showing relationships between vertices. A graph from discrete mathematics.
Graphs of the sort that we find in discrete mathematics are useful for solving problems concerning configurations and relationships.