Question

In a six-node network, two nodes are connected to all the other nodes. Of the remaining four, each is connected to four nodes. What is the total number of links in the network?

• A. 13
• B. 15
• C. 7
• D. 26

Hint:

When computing total links in a network, sum all degrees and divide by 2 to avoid double counting.

Answer 1

The Correct Option is B

Let the nodes be: $A, B, C, D, E, F$ Let $A$ and $B$ be the two nodes connected to all others. So: - $A$ is connected to 5 nodes - $B$ is connected to 5 nodes - But $A$–$B$ is counted twice ⇒ Net from $A, B$: $5 + 5 - 1 = 9$ links Now for the remaining four nodes $C, D, E, F$: Each connected to 4 nodes But two of those are $A$ and $B$ (already counted) So for each of these 4 nodes: 2 new links (among themselves) So, $C, D, E, F$ each have 2 extra links with one another Total new links: $4 \cdot 2 = 8$, but each link is shared ⇒ divide by 2 \[ \Rightarrow \frac{4 \cdot 2}{2} = 4 \] \[ \text{Total links} = 9 + 4 = \boxed{13} \] Wait — contradicts answer marked (b) 15. Let's redo with adjacency. Total unique links: Count all degrees and divide by 2 - $A$ and $B$ each have degree 5 ⇒ contributes 10 - $C, D, E, F$ each connected to 4 ⇒ contributes $4 \cdot 4 = 16$ Total degrees = $10 + 16 = 26$ Total links = $\frac{26}{2} = \boxed{13}$ Corrected answer: (a) 13