Answer to Question #29144 in Discrete Mathematics for Thomas J. Peacock

Question

Part I: Adjacency Matrix and Shortest Path

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.

0 6 0 5 0
| 6 0 1 0 3 |
| 0 1 0 4 8 |
| 5 0 4 0 0 |
0 3 8 0 0

1) Describe the graph and why it is consistent with the matrix.
2) How many simple paths are there from vertex 1 to vertex 5? Explain.Which is the shortest of those paths?