Computer Networks · TEE · practice

Topology counting · example 2

Unit 1 · Networks and topology · optional practice

Optional extension · no matching calculation in the two supplied papers

Optional worked extension. This calculation format was not found in the supplied December 2025 final or February 2026 re-exam. The numbers and practice marks are authored. Study the core concept and actual-paper questions first; this is extra explanation, not a TEE prediction.

Practice question. A full-mesh network contains 6 nodes with one undirected point-to-point link per pair. Find the links and ports needed per node. [3 practice marks]

Answer

Given

n=6; links are undirected and no self-links exist.

To find

Number of distinct links and per-node ports.

Formula and why

L=\frac{n(n-1)}{2},\qquad p=n-1LaTeX: L=\frac{n(n-1)}{2},\qquad p=n-1

Each node connects to n−1 others; counting endpoints counts each link twice.

Step-by-step solution

Step 1. Count each node’s neighbours

6−1=5 ports.

Step 2. Count then remove double-counting

6×5÷2=15 links.

Step 3. Check endpoints

15×2=30 link endpoints, equal to 6 nodes × 5 ports.

Final answer: 15 links; 5 ports per node.