Random Network - 20/03/2026

Given two networks:

  • Network A with \(N_{A}\)=50 nodes and \(P_{A}\)
  • Network B with \(N_{B}\)=100 nodes and \(P_{B}\)

Analyze these statements and find the values of X and Y

I. For both networks to share the same average degree, \(P_{A}\) should be approximately (1 decimal) X times \(P_{B}\)

II. Given that \(P_{A} = 0.5\) and \(P_{B} = 0.15\), you need to add Y nodes to A so they share the same average number of links

A) X=2, Y=5

B) X=2, Y=6

C) X=3, Y=7

D) X=3, Y=4

E) None of the above

Original idea by: Fernando de Facio Rossetti

Comentários

  1. Joao Meidanis21 de março de 2026 às 09:31

    Nice question, but there is too much work to be done to make it acceptable. First it has to say that the networks are generated by the G(N,p) model. Then I don't understand the (1 decimal)X part. Does it mean 1.X? If yes, why not write it like 1 + X/10? Finally, for Y, I believe we need (0.5)*(50+Y)*(50+Y-1)/2 = (0.15)*(100)*(100-1)/2 , which makes me think Y should be in the tens, not small values like the alternatives. I have to let it pass.

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