2021-041

Considering the following network and its partition in green and pink nodes:

The modularity $M$ of a partition can be computed using:

$$M=\sum _{c=1}^{n_c}[\frac{L_c}{L}-{\left(\frac{k_c}{2L}\right)}^2],$$

where $n_c$ is the number of sets in the partition and, for each set $S$, we denote by $L_c$ the number of links connecting two nodes in the set $S$, and by $k_c$ the sum of all degrees of nodes in $S$. What is the value of $M$ for the partition depicted above (round to 2 decimal places)?

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

Original idea by: Tiago Almeida