MathJax


Saturday, March 21, 2026

2026-330

Consider graphs with \(N = 4\) nodes. Below are three sample outcomes of \( G(N, p) \) at different values of \( p \). Dashed lines show absent edges.

Graph A Graph B Graph C

Which graph is in the supercritical regime?

(A) All three are supercritical since every node has at least one neighbor

(B) Graph A, because it has at least one edge and \( \langle k\rangle = 0.3 > 0 \)

(C) Graph B, because \(\langle k\rangle = 1 \) satisfies the condition for the giant component

(D) Graph C, because \( \langle k\rangle = 2.4 > 1 \) and \( p = 0.8 > p_c = 1/3 \)

(E) None of the above.


Original idea by: Gustavo P. C. P. da Luz

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