MathJax


Sunday, September 25, 2022

2022-163

Consider a network containing \(N\) nodes and with a minimum degree \(k_{min}\). If the degree distribution \(p_k\) follows a power law \(p_k \sim k^{-\gamma}\), where the exponent \(\gamma\) is the degree exponent, what is correct to affirm:

A. The average distance \(\langle d \rangle\) between two nodes is proportional to \(\ln N\) for \(2<\gamma\leq 3\).

B. The first moment \(\langle k \rangle\) diverges for \(2<\gamma\leq 3\).

C. The second moment \(\langle k^2 \rangle\) diverges for \(\gamma > 3\).

D. The expected size of the largest hub is \(k_{min}N^{\frac{1}{\gamma - 1}}\).

E. None of the above.

Original idea by: Marcelo Silva

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