Barabási: Ch. 7 — Degree Correlation

Consider a network with 4 nodes (1, 2, 3, 4) and the following 5 edges: (1, 2), (1, 3), (2, 3), (2, 4), (3, 4). What is the average nearest neighbor degree for nodes of degree $k=3$, denoted as $k_{nn}(3)$?

a) 2.5

b) 3.0

c) 2.67

d) 2.33

e) None of the above

Original ideia by: Gabriel Sato

Barabási: Ch. 5 — Barabási-Albert Model

Consider a network of N = 1000 nodes constructed using the Barabási–Albert (BA) model with parameter m = 3. We know that $\langle k \rangle = 2m = 6$ and $P(k) \sim k^{-3}$.

Now compare this network with an Erdős–Rényi network of the same size and same average degree, where the degree distribution is concentrated around $\langle k \rangle$.

Which alternative best describe the difference between these two types of networks?

a) In a BA network, the probability of finding nodes with degree much larger than 6 is significantly higher than in an Erdős–Rényi network.

b) In a BA network, all nodes tend to have degrees close to 6 just like in an Erdős–Rényi network.

c) In a BA network, the probability of high-degree nodes decays exponentially, while in Erdős–Rényi it follows a power law.

d) In both networks, the probability of hubs is practically the same.

e) None of the above


Original idea by: Gabriel Sato