Mesh Network Links for 8 Nodes Complete Graph Counting | AI Research

Mesh Network Links for 8 Nodes (Complete Graph Counting)

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Nov 3, 2026

In a fully connected mesh network (i.e., a complete graph), every pair of distinct nodes has exactly one dedicated point-to-point link. So the number of required links equals the number of unordered node pairs: $\binom{n}{2}=\frac{n(n-1)}{2}.$

For $n=8$ nodes: $\binom{8}{2}=\frac{8\cdot 7}{2}=28.$

Therefore, the correct option is (ii) 28.

Mermaid view (complete graph for 4 nodes, showing the idea of “one link per pair”):

Key terms:

mesh topology
complete graph
pairwise connection
unordered pair

Note: If links were directed (separate links for A→B and B→A), the count would double. The question says “every pair requires a dedicated point-to-point link,” which is standardly interpreted as one link per pair (undirected), matching $\binom{n}{2}$ .

Mesh/complete graph counting and combination formula reference: https://en.wikipedia.org/wiki/Complete_graph - Explains complete graphs and edge counts (edges = number of vertex pairs). ↩

Mesh topology and complete-graph intuition (pairwise connections)

Quick counting shortcut

For a fully connected mesh with $n$ nodes, remember: links = $n(n-1)/2$ . This directly counts “all pairs.”

Compute required links for 8-node fully connected mesh

1
Step 1
A fully connected mesh corresponds to a complete graph: one link per distinct node pair.
2
Step 2
Number of links equals $\binom{n}{2}=\frac{n(n-1)}{2}$ .
3
Step 3
Compute $\frac{8\cdot 7}{2}=28$ .
4
Step 4
28 corresponds to option (ii).

Links required for fully connected meshes (undirected)

Comparison shows the growth pattern using $\binom{n}{2}$ .

Common interpretation pitfalls

Knowledge Check

Question 1 of 4

Q1Single choice

A fully connected mesh with $n$ nodes requires how many undirected point-to-point links?

$\frac{n(n-1)}{2}$

$n^2$

$n(n-1)$

$\frac{n(n+1)}{2}$

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