2025-004

Consider a simple scale-free network generated through a configuration model with degree exponent γ = 2.4, minimum degree kₘᵢₙ = 1, and N = 10⁴ nós.

Suppose that the maximum degree is limited by the structural cutoff kₛ ~ N¹ᐟ², and that the empirical degree correlation function follows kₙₙ(k) ~ kᵘ.

Based on this scenario, select the correct statement:

A) The exponent μ < 0 arises solely from dynamic preferential attachment, since the configuration model preserves assortativity by construction.

B) Even though the configuration model is uncorrelated in principle, finite-size effects and the structural cutoff impose an effective dissortativity, resulting in μ < 0.

C) Increasing N while maintaining the same γ leads to stronger assortativity, because kₛ grows sublinearly with N.

D) Networks with γ < 3 cannot exhibit dissortative mixing, since their hubs dominate the connectivity pattern, forcing μ > 0.

E) None of the above.

Original idea by: Giancarlo Maldonado Cárdenas