Question for MO412 - 20/03/2026

Consider two random graphs, G_a and G_b, where edges are created independently with probabilities p_a and p_b, respectively. Additionally, consider the following binomial degree distribution:
 

Consider:  N_a = 200 and  N_b = 100 

Evaluate the following statements:

I) The average degree <k> is higher in graph G_b.  

II) The variance of the degree distribution in G_b  is greater than in G_a .  

III) The expected number of edges in G_a is greater than in G_b.  

Select the correct alternative:

A) Only I is correct.  

B) Only I and II are correct.  

C) Only II and III are correct.  

D) I, II, and III are correct. 

E) None of the above.


Original idea by: Gabriel Ukstin Talasso

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