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