If there are n devices (nodes) in a network, what is the number of cable links…
2017
If there are n devices (nodes) in a network, what is the number of cable links required for a fully connected mesh and a star topology respectively
- A.
n(n −1) / 2, n
- B.
n, n −1
- C.
n −1, n
- D.
n −1, n(n −1) / 2
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Correct answer: A
To determine the number of cable links, we analyze each topology separately. In a fully connected mesh topology, every device connects directly to every other device. For n devices, the number of unique connections is calculated using the combination formula C(n, 2), which simplifies to n(n − 1) / 2. This ensures full redundancy and direct communication between all nodes.\nIn a star topology, every device connects individually to a central hub or switch. Since each of the n devices requires one dedicated link to reach the center, exactly n cable links are needed. Therefore, the correct sequence is n(n − 1) / 2 for mesh and n for star. Option A matches this order perfectly.\nOther options are incorrect because they either swap the formulas or use linear counts where quadratic growth is required for a mesh. For instance, Option B suggests n links for mesh, which describes a ring or star, not a fully connected mesh.