Graphing Calc Interactive Scientific Calc
 Graphing Calc Interactive Scientific Calc

# Directed Graphs as matrices

Matrices can be used to represent pathways between points. This kind of matrix is known as a finite graph. When the paths have a direction (usually expressed as an arrow), the finite graph is known as a directed graph.
A directed graph is a set of points connected by paths. Paths are represented as lines or arrows. The points that are connected are called the vertices. The entries of a directed graph's matrix is either a "1" or a "0". That's it. "1" indicates that  a path exists. "0", on the other hand, indicates no path exists.

Pictured on the left are paths that a helicopter flew during its journey throughout the city.

At the bottom of the picture is a matrix representing the directed graph of the helicopter's journey.

In the matrix D on the left, a 0 indicates that no path exists between the two points. For instance, the plane never travels from A to C so entry D13 (marked in red) is 0 . On the other hand, since the plane travels from A to B , entry D12 in purble is 1 indicating that the plane did travel that path.

Practice Problems

Can you complete the matrix below to represent the directed graph on the left?