A fully connected network topology is a topology in which there is a direct…
2019
A fully connected network topology is a topology in which there is a direct link between all pairs of nodes. Given a fully connected network with \(𝑛\) nodes, the number of direct links as a function of \(𝑛\) can be expressed as
- A.
\(\frac{n(n+1)}{2}\) - B.
\(\frac{(n+1)}{2}\) - C.
\(\frac{n}{2}\) - D.
\(\frac{n(n-1)}{2}\)
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Correct answer: D
Answer: For a fully connected (undirected) network with n nodes, the number of direct links is n(n-1)/2.
Reasoning: Each node can be connected to every other node, so each node has (n-1) connections. Counting connections for all n nodes gives n(n-1).
Because each undirected link is counted twice in that product (once from each endpoint), divide by 2 to correct the double count.
Formula: n(n-1)/2
Example: n = 4 -> 4*3/2 = 6 links
Related notes: if self-connections are allowed the count becomes n(n+1)/2; for directed links without self-loops the count is n(n-1).
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