Putting It Together: Graph Theory
At the start of this module, you were thinking about finding the fastest route from one client to another. Thankfully, now you know how to use graph theory to figure it out. Take another look at the diagram. Now you know it is a graph in which each vertex represents a client and each edge represents a path between clients. The numbers, or weights, indicate the length of time (minutes) required to travel from one vertex to another.![Graph diagram connects locations A through E. A connects to B by 8 units, B to C by 8 units, C to D by 10 units, D to E by 8 units, E to F by 7 units, F to G by 5 units, G to H by 5 units, and H to I by 5 units. In addition, B connects to D by 14 units, B to F by 20 units, F to I by 15 units, and G to I by 12 units.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/1141/2017/03/29165259/graph1-300x216.png)
![Graph diagram connects locations A through E. A connects to B by 8 units, B to C by 8 units, C to D by 10 units, D to E by 8 units, E to F by 7 units, F to G by 5 units, G to H by 5 units, and H to I by 5 units. In addition, B connects to D by 14 units, B to F by 20 units, F to I by 15 units, and G to I by 12 units. A red 0 is placed near C, 10 by D, and 7 by B.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/1141/2017/03/29165408/graph2-300x216.png)
![Graph diagram connects locations A through E. A connects to B by 8 units, B to C by 8 units, C to D by 10 units, D to E by 8 units, E to F by 7 units, F to G by 5 units, G to H by 5 units, and H to I by 5 units. In addition, B connects to D by 14 units, B to F by 20 units, F to I by 15 units, and G to I by 12 units. A red 0 is placed near C, 10 by D, 7 by B, 27 by F, 15 by A, and 17 by I.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/1141/2017/03/29165457/graph3-300x216.png)
![Graph diagram connects locations A through E. A connects to B by 8 units, B to C by 8 units, C to D by 10 units, D to E by 8 units, E to F by 7 units, F to G by 5 units, G to H by 5 units, and H to I by 5 units. In addition, B connects to D by 14 units, B to F by 20 units, F to I by 15 units, and G to I by 12 units. A red 0 is placed near C, 10 by D, 7 by B, 27 by F, 15 by A, 17 by I, and 18 by E.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/1141/2017/03/29165621/graph4-300x216.png)
![Graph diagram connects locations A through E. A connects to B by 8 units, B to C by 8 units, C to D by 10 units, D to E by 8 units, E to F by 7 units, F to G by 5 units, G to H by 5 units, and H to I by 5 units. In addition, B connects to D by 14 units, B to F by 20 units, F to I by 15 units, and G to I by 12 units. A red 0 is placed near C, 10 by D, 7 by B, 25 by F, 15 by A, 17 by I, 18 by E, 27 by G, and 22 by H.](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/1141/2017/03/29165656/graph5-300x216.png)