The oscillations in a signal lying on a network can also be quantified by the number of zero crossings in the signal values. If there is a directed edge from node i to node j and there is a change in the sign of the signal values at nodes i and j, then it is counted as one zero crossing. Create a directed random network with 300 nodes by adding a directed edge between any two nodes with a probability of 0.15.
(a) Plot the number of zero crossings separately in real and imaginary parts of the eigenvectors
of the in-degree Laplacian matrix with respect to the magnitudes of the corresponding
eigenvalues. Comment on your observations and explain the frequency ordering.
(b) Repeat part (a) for the weight matrix of the network.
This problem is a computer-based exercise. You may use an appropriate software such Matlab
for solving this problem. Some useful code fractions can be found at the support website:
https://complexnetworksbook.github.io
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