Quiz - Random Networks

Consider \( N = 4 \) 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) 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

Comments

  1. Joao MeidanisMarch 21, 2026 at 10:58 AM

    Good question. I took it. Had to reorder the alternatives.

    ReplyDelete

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