The study of such graphs is called graph theory. Engineers need to find planarity in a graph when, for example, they are designing a computer chip without a crossed wire.

For example, a puzzle could have nine letters, shapes, or colors instead of numbers. When graph theorists label the vertices, they call it a “coloring.” A sudoku puzzle begins with a partial ...

The field of graph theory has been around since 1736, when Leonhard Euler published an article on the subject of the Seven Bridges of Königsberg (in Prussia, today’s Kaliningrad in Russia).

Graph theory may show how individuals are connected, for example, but not capture the ways in which clusters of friends on social media influence each other’s behavior.