Final answer:
The correct answer is Option D. The total number of links in the six-node network is 26. This is determined by adding the connections of the two nodes linked to all others with the interconnections of the remaining four nodes and their links to the first two.
Step-by-step explanation:
The question given involves calculating the total number of links in a six-node network with specific connectivity conditions. Let's break down the network connections:
- Two nodes are connected to all the other nodes, which adds up to 2*(6-1) = 10 links (each of the two nodes has 5 links).
- The remaining four nodes are connected to four nodes each. However, since each of these connections is between two of the four nodes, we must avoid double-counting. Therefore, for these four nodes, we have 4*(4/2) = 8 links (each connection is counted once for the two nodes it connects).
Now, we combine the two sets of links to get the total number of links in the network:
10 (from the first two nodes) + 8 (from the remaining four nodes) = 18 links.
However, this does not account for the additional links that the remaining four have with the first two, which are already connected to all other nodes. Each of the remaining four will have one link to each of the two fully connected nodes, adding 4*2 = 8 additional links.
Adding these to our previous total:
18 + 8 = 26 links in the network.
So, the correct answer is (d) 26.