Determine the Laplacian Matrix L.

Using an eigenvalue/eigenvector calculator, determine theFielder eigenvector corresponding to the secondsmallest eigenvalue of the Laplacian L(the first smallesteigenvalue is always equal to 0). Show the matrix used for thecalculation (cut and paste) and the eigenvector obtained from thecalculator.

Plot the eigenvector where the X-axis are the nodes of the planeand Y axis is the entry corresponding in the eigenvector to thatnode. Example for eigenvector u = (-0.4, -0.5, 0, 0.2, 0.7) thecoordinates(1, -0.4), (2,-0.5)....etc., should be plotted.

Explain how two clusters are found using the plotted graph.

From the plotted graph, could you explain how to get 3 clustersby partitioning one of clusters found in the previous step intotwo. Explain

0.3 1 0.1 3 0.3 0.4 0.1 0.3 0.2 4 2 5 0.3 0.2