# Topology counting · example 3

Subject: Computer Networks

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/cn/#tee/practice/introduction/mesh-3

Canonical: https://deep-learning-study-room.vercel.app/read/cn/tee/practice/introduction--mesh-3/

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

#### Answer

## Given

n=8; 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

8−1=7 ports.

#### Step 2. Count then remove double-counting

8×7÷2=28 links.

#### Step 3. Check endpoints

28×2=56 link endpoints, equal to 8 nodes × 7 ports.

**Final answer:** 28 links; 7 ports per node.

#### What this result means

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