<｜begin▁of▁sentence｜>### Instruction:
As a screenwriter crafting the storyline for a new TV series about detectives solving complex puzzles, you're tasked with ensuring the accuracy of the detectives' methods for analyzing evidence. In one scene, Detective Smith uses a cutting-edge algorithm to represent clues as graphs, aiding in the investigation. Now, you need to develop a dialogue between Detective Smith and her colleague, Detective Jones, to verify if two sets of evidence, represented as path graphs with 5 vertices each, exhibit the same connections.

Smith: "Jones, I need your expertise. We've got two sets of evidence, each mapped out as path graphs with 5 vertices. I need to determine if their adjacency matrices match up."

Jones: "Hmm, that sounds like a job for our Matrix class comparison method. We can employ the '__eq__' method from our Matrix API to check for exact equivalence between the adjacency matrices. Let's get started."

Smith: "Right, so we'll feed the adjacency matrices of both graphs into the '__eq__' method, and if it returns True, it means the matrices are identical."

Jones: "Precisely. If True, it suggests that the connections between vertices in both graphs are the same, indicating a potential correlation between the two sets of evidence."

Smith: "Excellent. Let's run the comparison and see if we're dealing with two pieces of the same puzzle or if we've got entirely different leads to pursue."
### Response:
from networkx.linalg.graphmatrix import adjacency_matrix
import networkx as nx

# Create two graphs
g1 = nx.path_graph(5)
g2 = nx.path_graph(5)

# Get the adjacency matrices as Scipy sparse matrices
A1 = adjacency_matrix(g1)
A2 = adjacency_matrix(g2)

# Compare the matrices
equal_matrices = (A1 != A2).nnz == 0
print('Are the matrices equal?', equal_matrices)
<|EOT|>
