📚 Part 1: Understanding Network Diagrams

1. A connected graph is a graph where there is a path between every pair of vertices. Circle the correct answer:

True

False

2. Which of the following best describes a non-connected graph?

All vertices are connected to each other

At least one pair of vertices has no path connecting them

The graph has exactly 5 vertices

The graph forms a perfect circle

3. Look at the network diagram below representing a friendship network. Is this graph connected or non-connected? Explain your reasoning.

Network: A connects to B, B connects to C, D connects to E

4. Give one real-world example each of:

a) A connected network: ________________

b) A non-connected network: ________________

✏️ Part 2: Drawing Network Diagrams

5. Draw a connected graph with 4 vertices (A, B, C, D) where each vertex has at least 2 connections.

6. Draw a non-connected graph with 5 vertices that has exactly 2 separate components.

7. A social media network has the following connections:
• Sarah is friends with Tom and Lisa
• Tom is friends with Sarah and Mike
• Lisa is friends with Sarah only
• Mike is friends with Tom only
• James has no friends in this network
Draw this network diagram below:

📊 Part 3: Adjacency Matrices

8. Complete the steps to convert a network diagram into an adjacency matrix:

Step 1: List all ________ as both row and column headers

Step 2: Place a '____' if there is an edge connecting two vertices, otherwise place a '____'

Step 3: ________ the matrix to analyse network properties

9. For the network where A connects to B, B connects to C, and A connects to C, complete the adjacency matrix:

A B C

A [ __ __ __ ]

B [ __ __ __ ]

C [ __ __ __ ]

10. Look at this adjacency matrix and draw the corresponding network diagram:

X Y Z

X [ 0 1 1 ]

Y [ 1 0 0 ]

Z [ 1 0 0 ]

⚖️ Part 4: Weighted Networks and Tables

11. In a weighted network, edges have values called weights that represent things like distance, cost, or time. When converting a weighted network to an adjacency matrix (table), we write the weight values in the cells instead of just 1 or 0.

12. Look at this example of a weighted adjacency matrix showing distances between cities:

London Paris Rome

London [ 0 344 1435 ]

Paris [ 344 0 1107 ]

Rome [1435 1107 0 ]

What does the value 344 represent? ________________

13. Convert this weighted network diagram to an adjacency matrix:

Network: A connects to B (weight 5), A connects to C (weight 3), B connects to C (weight 7)

A B C

A [ __ __ __ ]

B [ __ __ __ ]

C [ __ __ __ ]