Random Graph - Erdős-Rényi

Consider a connected Erdős-Rényi random graph \( G(n, p) \) with \( n = 100 \) nodes and edge probability \( p = 0.1 \). The average degree is \( \langle k \rangle = 10 \). Which of the following statements is correct?

  1. The degree distribution is concentrated around the mean, the average distance scales linearly with \( n \), and the clustering coefficient is \( 0.05 \).
  2. The degree distribution is approximately Poisson, the average distance is 2, and the clustering coefficient is roughly equal to \( p \).
  3. The degree distribution is uniform, the average distance is independent of \( n \), and the clustering coefficient grows with \( n \).
  4. The degree distribution is Poisson, the average distance is 3, and the clustering coefficient is zero.
  5. None of the above

Original idea by: Aline Azevedo

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