Computer Networks · TEE · practice

Topology counting · example 1

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 4 nodes with one undirected point-to-point link per pair. Find the links and ports needed per node. [3 practice marks]

Answer

Given

n=4; 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

4−1=3 ports.

Step 2. Count then remove double-counting

4×3÷2=6 links.

Step 3. Check endpoints

6×2=12 link endpoints, equal to 4 nodes × 3 ports.

Final answer: 6 links; 3 ports per node.