Consider a network with 6 routers R1 to R6 connected with links having weights…

Solution

After changing the previously unused links to weight 2, the updated network has link costs:

• R1–R2 = 2

• R1–R3 = 3

• R2–R3 = 2

• R2–R4 = 7

• R3–R5 = 9

• R4–R5 = 1

• R4–R6 = 2

• R5–R6 = 4

When shortest paths are recomputed, the link R5–R6 (cost 4) is never preferred because there is always a cheaper alternative through R4:

• R5 → R6 directly = 4

• R5 → R4 → R6 = 1 + 2 = 3

Since cost 3 is less than cost 4, any shortest path that might use R5–R6 instead uses R5–R4–R6.

All other links participate in at least one shortest path, but R5–R6 (cost 4) does not.

Therefore, exactly one link remains unused.

Hence, the correct answer is:

Option B) 1