2021-039

Consider the two partitions below on the same network:

What are the modularities \( M_a \) and \( M_b \) of the partitions in pictures \( a \) and \( b \), respectively? Round the result to two decimal places, if necessary.

1. \( M_a = 0.20 \) and \( M_b = 0.30 \)
2. \( M_a = 0.20 \) and \( M_b = 0.34 \)
3. \( M_a = 0.24 \) and \( M_b = 0.30 \)
4. \( M_a = 0.24 \) and \( M_b = 0.34 \)
5. None of the above.

Original idea by: Bruno Almêda