# Topology counting · example 1

Subject: Computer Networks

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/cn/#tee/practice/introduction/mesh-1

Canonical: https://deep-learning-study-room.vercel.app/read/cn/tee/practice/introduction--mesh-1/

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



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



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.

#### What this result means

Supporting topology arithmetic: a directed-arc count would be n(n−1), so read the link convention.