1. Identify the two communities in the dolphins data set by obtaining the Fiedler vector of the normalised Laplacian. Provide a visualisation of the outcome so that the names of the dolphins, the network, and the two communities are clearly visible. Indicate the approach you have taken in light of the fact that the two communities are of different sizes.
2. Use the Louvain method to identify the two communities. Provide a picture similar to the one you generated in question 1.
3. Follow the method outlined in slide 31 to generate the "adjacency" matrix. Choose the top two eigenvectors and use the k-means algorithm on the rows to arrive at your two clusters. Provide a picture of your outcome to demonstrate that the circles have been captured.
You can use existing Python packages (for eigenvectors, k-means, etc., but the spectral clustering algorithm implementation should be yours).