Network Diagrams Worksheet

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📚 Part 1: Definitions and Concepts

1. Define a connected graph in your own words.

2. What are isomorphic graphs? Explain why they are considered equivalent.

3. Which of the following statements about connected graphs is TRUE?

A connected graph must have exactly one path between any two vertices

In a connected graph, there is at least one path between any two vertices

A connected graph cannot have cycles

A connected graph must be a complete graph

4. Two graphs are isomorphic if they have the same:

Number of vertices

Number of edges

Degree sequence

Visual appearance

🔍 Part 2: Analysis Tasks

5. For each network diagram below, determine if it is CONNECTED or DISCONNECTED. (Imagine simple network diagrams A, B, and C are provided)

Network A: ________________

Network B: ________________

Network C: ________________

6. Given pairs of network diagrams (imagine diagrams are provided), identify which pairs are ISOMORPHIC. Circle your answers.

Pair 1: Graphs D and E

Pair 2: Graphs F and G

Pair 3: Graphs H and I

None of the pairs are isomorphic

7. Explain your reasoning for identifying the isomorphic pair in Question 6.

🌐 Part 3: Practical Application

8. Create a small network diagram representing social media connections between 6 people. Use the space below to draw your network, labelling each vertex with a person's name (can be fictional).

9. Analyse your network from Question 8:

a) Is your network connected? _____________ Explain why: _________________________________

b) How many edges does your network have? _____________

c) What is the degree of the most connected person? _____________

10. Could you redraw your network from Question 8 in a different layout while keeping it isomorphic? Briefly explain how.

11. Why is understanding connectivity important in real-world networks? Give one specific example.

12. Reflection: How might isomorphism be useful when analysing large networks like the internet or transportation systems?

Network Diagrams Worksheet

Network Diagrams Worksheet

📚 Part 1: Definitions and Concepts

🔍 Part 2: Analysis Tasks

🌐 Part 3: Practical Application

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