The picture above shows our game represented as a graph — a collection of points (called vertices) and segments between them (called edges). The dilemma you face exemplifies a simple but profound idea ...

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 ...

To illustrate the kinds of relationship that a hypergraph can tease out of a big data set — and an ordinary graph can’t — Purvine points to a simple example close to home, the world of scientific ...

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.

In theory, it cannot be ruled out that the algorithms might run for longer than the age of the universe. But in practice, ...

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.