2025-262

Define f(N,γ) as the function that computes the second moment of the degree distribution, ⟨k²⟩ , for a finite, scale-free network with N nodes with minimum degree k_min​ = 1 and degree exponent γ. Use the Continuum Formalism.

Compute the following ratios:

1. f(10⁴, 7/3) / f(10⁴, 5)

2. f(10⁸, 7/3) / f(10⁸, 5)

3. f(10¹², 7/3) / f(10¹², 5)

The values for (1), (2), and (3) are approximately, respectively:

A. 1, 10_000,  1_000_000_000
B. 1, 100_000_000, 1_000_000
C. 100, 10_000, 1_000_000
D. 100, 100_000_000, 1_000_000_000
E. None of the above

Note: underscores are used for readability of large numbers.

Original idea by: Rodolfo Bitu