Question 6. Modularity

 

Imagine a Cayley Tree, constructed starting from a central node of degree k. Each node at distance d from the central node has degree k, until the nodes reachable at distance P that have degree one, as shown in figure above. Consider that there are k+1 communities, where each community corresponds to a leaf of the network and the central node is other community. Considering that the number of nodes reachable in t steps from the central node is computed as k(k-1)t-1, and  number of links L = N-1, being N the number of nodes, what is the modularity if k=3 and t=4? Round it up to three decimals places.

Tip: Try to model the total number of links within the community, Lc, and the total degree of the nodes in the community kc as a function of k and t.

A. 0.621

B. 0.523

C. 0.785

D. 0.591

E. None of the above.

Original idea by: Germán Darío Buitrago Salazar


Comentários

  1. Joao Meidanis4 de junho de 2023 às 06:34

    My calculations resulted in 0.621, which is close but not equal to (A). Contributions of the communities where -1/900 and three times 1679/8100. Did I do something wrong?

    ResponderExcluir
    Respostas
    1. Germán Darío Buitrago Salazar4 de junho de 2023 às 08:17

      Hi Professor. Yes, the answer is 0.621. Iwas wrong when I was writing the blog. I am going to correct it.

      Excluir
  2. Joao Meidanis10 de junho de 2023 às 03:00

    Ok! Thanks! I'll take it!

    ResponderExcluir

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