2025-257

\(G_1(N,p_1)\) and \(G_2(N,p_2)\) are two random networks with the same number of nodes \(N\), but different link probabilities, with \(p_1 > p_2\).

Which of the following statements is correct?

1. \(G_1\) will have a lower clustering coefficient than \(G_2\).
2. \(G_2\) will have a larger average degree than \(G_1\).
3. Both \(G_1\) and \(G_2\) must have the same degree distribution, since they share the same number of nodes \(N\).
4. \(G_1\) is more likely to contain a giant component than \(G_2\).
5. None of the above.

Original idea by: Gabriel Sato