I have to write 2 page document with supporting graph on the question below

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Mathematics

Description

Construct a graph based on the adjacency matrix that appears below. Label all nodes with indices consistent with the placement of numbers within the matrix. Then, answer the questions that follow.

| 0 3 6 8 5 2 |
| 3 0 4 9 0 0 |
| 6 4 0 4 0 0 |
| 8 9 4 0 2 0 |
| 5 0 0 2 0 0 |
| 2 0 0 0 0 0 |

  1. How many simple paths are there from vertex 1 to vertex 4?
  2. Which is the shortest of those paths? How did you determine that?


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