For n devices in a network, how many full-duplex point-to-point links are…
2014
For n devices in a network, how many full-duplex point-to-point links are required in a full mesh topology?
Answer: D. n(n − 1)/2 — ConceptIn a full mesh topology, every unordered pair of distinct devices has one direct point-to-point link. A full-duplex link carries traffic in both…
- A.
n(n + 1)
- B.
n(n − 1)
- C.
n(n + 1)/2
- D.
n(n − 1)/2
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Show answer & explanation
Correct answer: D
Concept
In a full mesh topology, every unordered pair of distinct devices has one direct point-to-point link. A full-duplex link carries traffic in both directions, so the same device pair needs one physical link, not two directional links.
Application
Each of the n devices is incident to n − 1 links, giving n(n − 1) link-ends in total.
Every physical link has two ends and is therefore counted once from each endpoint.
Dividing the link-end count by 2 gives n(n − 1)/2 physical full-duplex links.
Cross-check
For n = 4, the unordered pairs are {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}: six links. The formula gives 4 × 3 / 2 = 6.
Result
Therefore, a full mesh of n devices requires n(n − 1)/2 full-duplex point-to-point links.
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