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**Adjacency Matrix and Shortest Path** on
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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⌋

Describe the graph and why it is consistent with the matrix.

How many simple paths are there from vertex 1 to vertex 5? Explain.Which is the shortest of those paths?