Consider a one dimensional lattice with N nodes that form a circle, where each node connects to its two neighbors. Partition the line into nc consecutive clusters of size Nc=N/nc.




According to the Maximum Modularity Hypothesis, the maximum of Mc corresponds to the best partition. Obtain the community size nc corresponding to the best partition when N=15.

A) nc = 5
B) nc = 3.87
C) nc = 0.97
D) nc = 5.47
E) None of the above

Original idea from https://networksciencebook.com/chapter/9#homework9

Author: Raphael Adamski

Comentários

  1. Raphael Adamski15 de novembro de 2025 às 07:17

    Professor, inicialmente eu tentei fazer este exercício usando uma Cayley Tree, porem ficou muito complexo a inferencia de lc (links dentro da communidade) e tambem a derivacao para maximizar a modularidade em funcao do grau k da arvore, entao fiz o exercicio usando o mesmo do livro com mais imagens e um N fixo para facilitar a vida do aluno

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