Barabási: Ch. 4 — Scale Free Networks

 In scale-free networks, the maximum degree grows with the size of the network as a power of the total number of nodes.

Suppose you have a scale-free network with $\gamma = 2.5$ and a total of $N = 10^6$ nodes. Which of the following best approximates the maximum degree in the network?

a) $N^{0.5} \approx 10^3$

b) $N^{1/3} \approx 10^2$

c) $N^{2/3} \approx 10^4$

d) $N^{1.5} \approx 10^9$

e) None of the above

Original idea by: Gabriel Sato

Barabási: Ch. 3 — Random Networks

$G_1(\mathrm{N,}{p}_1)$ and $G_2(\mathrm{N,}{p}_2)$ are two random networks with the same number of nodes $\mathrm{N,\; but\; different\; link\; probabilities\; with }$$p_1>p_2$. 

Which of the following statements is correct?

a) $G_1$will have a lower clustering coefficient than $G_2$.

b) $G_2$ will have a larger average degree than $G_1$.

c) $G_1$is more likely to contain a giant component than $G_2$.

d) Both $G_1$and $G_2$must have the same degree distribution, since they share the same $\mathrm{number\; of\; nodes\; N.}$

e) None of the above

Original idea by: Gabriel Sato