Gustavo Luz Blog

The figure below shows the Complementary Cumulative Distribution Function (CCDF) $P(K > k)$ on a log-log scale for two networks, both with $N = 10^4$ nodes and $k_{\min} = 1$. Network A has $\gamma = 2.1$ and network B has $\gamma = 2.9$.   In what range does the ratio ($r$) of the largest hub in network A to the largest hub in network B fall? $0 \leq r \lt 10$ $10 \leq r \lt 20$ $20 \leq r \lt 30$ $30 \leq r \lt 40$ None of the above Original idea by: Gustavo P. C. P. da Luz

Consider \( N = 4 \) nodes. Below are three sample outcomes of \( G(N, p) \) at different values of \( p \). Dashed lines show absent edges. Which graph is in the supercritical regime? (A) Graph A, because it has at least one edge and \( \langle k \rangle = 0.3 > 0 \) (B) Graph B, because \( \langle k \rangle = 1 \) satisfies the condition for the giant component (C) Graph C, because \( \langle k \rangle = 2.4 > 1 \), so \( p = 0.8 > p_c = 1/3 \) (D) All three are supercritical since every node has at least one neighbor (E) None of the above. Original idea by: Gustavo P. C. P. da Luz

 Consider the four graphs below: Which graph has the highest average clustering coefficient C, and what is its value? A) Graph 1, with C = 0 B) Graph 4, with C = 0.47 C) Graph 2, with C = 0.50 D) Graph 3, with C = 0.10 E) None of the above Original idea by: Gustavo P. C. P. da Luz