Question 38

In modular design:

• Cohesion measures the degree of internal binding within a module, characterized here by the number of access edges between methods and attributes belonging to the same module.
• Coupling measures inter-module dependencies, characterized by access edges crossing between a method in one module and an attribute in another module.

From the given access graph:

• Method $m$ is initially in module $M_1$. It accesses 2 attributes in $M_1$ and 2 attributes in $M_2$.
  • The 2 edges to attributes in $M_1$ are internal to $M_1$ (cohesion of $M_1$).
  • The 2 edges to attributes in $M_2$ are cross-module edges (coupling between $M_1$ and $M_2$).

Now suppose method $m$ is moved to module $M_2$ while leaving all attributes where they are:

• The 2 edges from $m$ to attributes in $M_2$ are now internal to $M_2$ (cohesion of $M_2$).
• The 2 edges from $m$ to attributes in $M_1$ are now cross-module edges (coupling between $M_2$ and $M_1$).

Comparing the totals:

1. Total internal edges across both modules:
   • Before: $E_{\text{int}}(M_1) + E_{\text{int}}(M_2)$, which includes 2 edges from $m$ inside $M_1$.
   • After: $(E_{\text{int}}(M_1) - 2) + (E_{\text{int}}(M_2) + 2) = E_{\text{int}}(M_1) + E_{\text{int}}(M_2)$. The total number of internal edges across the system is unchanged, so the average cohesion remains the same.
2. Total cross-module edges:
   • Before: 2 edges from $m$ crossed from $M_1$ to $M_2$.
   • After: 2 edges from $m$ cross from $M_2$ to $M_1$.
   • The total number of cross-module edges is unchanged, so coupling between modules remains the same.

Therefore, there is no change in either average cohesion or coupling.