Considering the following network:


This network clearly has two communities with the same quantity of nodes. One way to check if a network really has communities, i.e., it was not created by chance, is to check the modularity of all partitions of the network. The modularity can be check using: $M=\sum_{c=1}^{n_c} \left[ \frac{L_c}{L}- \left( \frac{k_c}{2L} \right)^2 \right]$. The higher is $M$ for a partition, the better is the corresponding community structure. Thus, what is the value of $M$ for the network in the picture?

  1. $M=0$
  2. $M=-0.5$
  3. $M=0.45$
  4. $M=-0.12$
  5. None of the above


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