Gustavo Luz Blog

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