Generate three connected ER graphs: G 1 (with edge probability of 0.2), G 2 (with edge prob- ability of 0.25), and G3 (with edge probability of 0.3), each having 50 nodes. Define three graph signals: f1 = u 0 on graph G 1 , f2 = u24 on graph G 2, and f3 = u49 on graph G 3. Now connect the three graphs by adding six additional edges to form a single connected graph G . Consider signal f = [ f1 T f2 T f3 T ] T on graph G
(a) Plot the GFT coefficients of signal
f. Do they convey any information about the local
frequency content of the signal f supported by graphs
G1,G2, andG3? Why or why not?
(b) Plot and explain the spectrogram of graph signal
f assuming a heat kernel g^(?`) = ae?k?`;
choose the constants a and k such that ||g||2 = 1.
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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Answer the following statement true (T) or false (F)
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The first value in a linear trend is 50 and the fifth value is 475. What are the values of the second, third, and fourth items?
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