All the routers use the distance vector based routing algorithm

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Direction: Consider a network with 6 routers R₁ to R₆ connected with links having weights as shown in the following diagram.

All the routers use the distance vector based routing algorithm to update their routing tables. Each router starts with its routing table initialized to contain an entry for each neighbour with the weight of the respective connecting link. After all the routing tables stabilize, how many links in the network will never be used for carrying any data?

1. 4
2. 3
3. 2
4. 1

Correct Option: C

We can check one by one all shortest distances. When we check for all shortest distances for Ri we don't need to check its distances to R0 to Ri-1 because the network graph is undirected.
Following will be distance vectors of all nodes.
Shortest Distances from R1 to R2, R3, R4, R5 and R6 R1 (5, 3, 12, 12, 16)
Links used : R1-R3, R3-R2, R2-R4, R3-R5, R5-R6
Shortest Distances from R2 to R3, R4, R5 and R6 R2 (2, 7, 8, 12)
Links used : R2-R3, R2-R4, R4-R5, R5-R6
Shortest Distances from R3 to R4, R5 and R6 R3 (9, 9, 13)
Links used : R3-R2, R2-R4, R3-R5, R5-R6
Shortest Distances from R4 to R5 and R6 R4 (1, 5)
Links used : R4-R5, R5-R6
Shortest Distance from R5 to R6 R5 (4)
Links Used : R5-R6
If we mark, all the used links one by one, we can see that following links are never used.
R1-R2
R4-R6