2. Generate a connected symmetric random network with arbitrary structure. Choose the size N as you like (but at least greater than 4). Calculate all the Laplacian eigenvalues of the Laplacian matrix Lij = Aj - kidij, where Aij is the adjacency matrix and ki is the degree of node i. Numerically integrate a network diffusion equation N ti(t) = Lili (i = 1, ...,N) j=1 from some non-uniform initial condition and show that all 2, eventually converge to the same value 2. Calculate d(t) = 2(Ez(t) )2 as the measure of non-uniformity and plot d(t) as a function of the time t. Evaluate the long-term convergence rate and compare it with the second Laplacian eigenvalue. 2. Generate a connected symmetric random network with arbitrary structure. Choose the size N as you like (but at least greater than 4). Calculate all the Laplacian eigenvalues of the Laplacian matrix Lij = Aj - kidij, where Aij is the adjacency matrix and ki is the degree of node i. Numerically integrate a network diffusion equation N ti(t) = Lili (i = 1, ...,N) j=1 from some non-uniform initial condition and show that all 2, eventually converge to the same value 2. Calculate d(t) = 2(Ez(t) )2 as the measure of non-uniformity and plot d(t) as a function of the time t. Evaluate the long-term convergence rate and compare it with the second Laplacian eigenvalue