Consider the graph in Figure 1. b g (h) Figure 1: A graph for spectral clustering....

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Consider the graph in Figure 1. b g (h) Figure 1: A graph for spectral clustering. 1. Represent this graph as an adjacency matrix with 1 if there is an edge, and 0 otherwise. 2. Compute the Laplacian matrix of the graph. 3. Show the eigenvectors of the Laplacian matrix sorted in ascending order according to their corresponding eigenvalues. (You may use numpy for this part.) 4. Use the second eigenvector v2 (corresponding to the second smallest eigenvalue) to find two clusters in the graph. 5. Now use the eigenvectors v2 and v3 to find three clusters in the graph. Consider the graph in Figure 1. b g (h) Figure 1: A graph for spectral clustering. 1. Represent this graph as an adjacency matrix with 1 if there is an edge, and 0 otherwise. 2. Compute the Laplacian matrix of the graph. 3. Show the eigenvectors of the Laplacian matrix sorted in ascending order according to their corresponding eigenvalues. (You may use numpy for this part.) 4. Use the second eigenvector v2 (corresponding to the second smallest eigenvalue) to find two clusters in the graph. 5. Now use the eigenvectors v2 and v3 to find three clusters in the graph.