Copying Model Question

 A friend of yours has published a pioneering research paper in a niche area, and it has gathered several citations from other researchers. The directed graph below shows the citation relationships among papers in this area.


Your friend is extremely happy with the results, given that his Paper A is already the most influent paper in the network, with an incoming degree of 4. Curious, with your knowledge on network science, you want to understand what the probability of a new paper is citing paper A. 

You are happy with rough approximations, so you frame this problem using a copying model of a directed network. With the probability of linking uniformly at random to an existing paper of p = 0.4, and the probability of copying of a link from a random citation of 1 - p, what is the probability of a new paper connecting to paper A? Round to two decimal places.

a) 0.1

b) 0.20

c) 0.29

d) 0.21

e) None of the above


Original idea by: Alexandre Petrachini


Comentários

  1. Joao Meidanis5 de outubro de 2025 às 02:43

    Bela questão, só que, pelas minhas contas a resposta é E. Confere?

    ResponderExcluir
  2. Alexandre Petrachini5 de outubro de 2025 às 12:51

    A opção correta seria a D professor, pelo menos de acordo com o meu racícionio.

    p = 0.4
    N = 10
    L = 14
    degree of A = 4

    Olhando a formula deste capitulo: https://networksciencebook.com/chapter/5#origins:~:text=degree%2Dk%20node-,follows,-%CE%A0(k

    Temos que modificar a formula pois k/2L é para redes não direcionadas. Utilizando kin/L obtemos:

    Π(i)= p/N ​+ (1−p)*kin/L​​.
    colocando os valores: 0.4/10 + (0.6)*4/14 resulta em 0.21

    Se houver algum erro na lógica me avise

    ResponderExcluir

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