A graph is a visual plotting of the relationship between two or more quantities, like a math map. To graph is to create such a chart.
The noun graph came into use in the 1800s, when people got tired of saying graphic formula and decided to chop it down. A hundred years later, the verb form of graph was first recorded. Diagram and linear representation are two synonyms for the word. The dancer Martha Graham said, “Every dance is a kind of fever chart, a graph of the heart.” Here, she uses graph to say that dance is a visual representation of what’s in the heart.