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LTE ass: Distribute ted Algorithms and Network Sys l 2017 We homework-we... You need to use Matlab or some other software (Octave, Scilab.) Exercise 1 (Laplacian of undirected graph): 1. Draw a connected undirected graph of order 6 2. Write its Laplacian matrix L 3. Find numerically the eigens of L, and verify that . L is positive semi-definite, .e., its eigenvalues are all non-negative; . the eigenvalues of L belong to the region given by Gershgorin circle theorem; the zero eigenvalue has the multiplicity that you expect from theory. Exercise 2 (Continuous-time consensus on undirected graph): Consider the same graph as in Exercise 1 . Assign to each node an initial state r(0) . Plot the trajectories ai(t)..o the dynamical system Comment the plot: do trajectories converge? if so, do they all converge to a same point consensus) or to different ones: what is/are such value(s)? is the average ,B(t) constant in time? Check that all answers are consistent with the theory seen in class Exercise 3: Repeat Ex. 2 but with a graph having two connected components. Exercise 4 (Directed raphs Part 1): Consider the following digraphg