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Difficulty: HardNetwork Topologies and Types

An enterprise architecture team is redesigning the physical WAN connections between 55 regional facilities. Currently, all 55 sites are interconnected using a fully meshed topology of dedicated point-to-point links to guarantee fault tolerance. To reduce recurring leased-line costs, management requests transitioning to a partial-mesh design that decommissions as many links as possible while guaranteeing that every site still retains at least two physically independent transmission paths to reach any other site. What is the maximum number of point-to-point links that can be decommissioned from the original network design?

  1. 5 linksAnswer
  2. B
    6 links
  3. C
    4 links
  4. D
    3 links

Answer

5 links can be decommissioned from the original full-mesh deployment.
For a network of 55 sites (n=5n=5), a full-mesh topology requires n(n−1)2=5×42=10\frac{n(n-1)}{2} = \frac{5 \times 4}{2} = 10 links. To guarantee that every site maintains at least two independent pathways to every other site, the minimum viable partial-mesh layout is a ring topology requiring 55 links. Subtracting the 55 required links from the original 1010 links allows maximum decommissioning of 55 links.

Step-by-Step Solution

1
Calculate total point-to-point links in the existing full-mesh topology
Using the formula L=n(n−1)2L = \frac{n(n-1)}{2} where n=5n = 5: L=5×42=10L = \frac{5 \times 4}{2} = 10 physical links.
Full mesh requires a direct point-to-point cable run between every unique pair of nodes.
2
Determine the minimum number of links needed to satisfy the dual-path redundancy constraint
A minimum of 55 links configured in a closed ring (partial mesh) topology.
In a ring topology with n=5n = 5 nodes, every node has a degree of 2 (connected to two neighbors), providing two distinct physical paths (clockwise and counter-clockwise) to reach any destination node.
3
Subtract the required partial-mesh link count from the original full-mesh link count
10 links (full mesh)−5 links (ring partial mesh)=5 links decommissioned10 \text{ links (full mesh)} - 5 \text{ links (ring partial mesh)} = 5 \text{ links decommissioned}.
This yields the maximum number of links that can be removed while preserving fault tolerance constraints.

Key Concept

Full Mesh vs Partial Mesh Link Calculations
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Topics

Network Topologies and Types

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