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Network Diagrams Notes

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Network Diagrams Notes

Network diagram illustration

📚 Key Definitions and Concepts

Network Diagrams

A network diagram (or graph) consists of:

  • Nodes (vertices): Points representing objects or entities
  • Edges: Lines connecting nodes, showing relationships

Connected vs Non-Connected Networks

1. Fill in the missing words:

A connected graph is one where there is a __________ between every pair of vertices. This means you can reach any vertex from any other vertex by following the edges.

2. Complete the definition:

A non-connected graph (disconnected) has at least one pair of vertices with __________ connecting them, creating separate __________ or components.

3. Which of these represents a connected network?

A transport network where some towns cannot be reached from others

A friendship network where every person is linked directly or indirectly to everyone else

A computer network with isolated clusters

Key Terms

4. Match each term with its correct definition:
Isomorphic graphs
Connectivity
Components
Weighted network
Separate parts of a disconnected graph
Graphs with identical structure but different appearance
A network where edges have numerical values
Whether vertices can reach each other via paths

✏️ Drawing Network Diagrams

Steps to Create a Network Diagram:

  1. Identify nodes: List all entities/objects
  2. Draw nodes: Use circles or dots, label clearly
  3. Add edges: Draw lines between connected nodes
  4. Label edges: Add weights/values if needed
5. Draw a network diagram for this scenario:

Four friends: Alex, Ben, Claire, and Dana. Alex knows Ben and Claire. Ben knows Alex and Dana. Claire knows Alex and Dana. Dana knows Ben and Claire.

6. Is your diagram from Question 5 connected or non-connected? Explain:
7. Draw a non-connected network with 5 nodes:

📊 Adjacency Matrices

Converting Network Diagrams to Tables

An adjacency matrix is a table showing connections between nodes:

  • Rows and columns represent nodes
  • Enter '1' if nodes are connected, '0' if not
  • For weighted networks, enter the weight value instead of '1'
8. Complete this adjacency matrix for the network: A connects to B and C, B connects to A and C, C connects to A and B:
ABC
A0______
B___0___
C______0
9. What do you notice about the diagonal of an adjacency matrix? Why?
10. Create an adjacency matrix for your diagram from Question 5:
11. How would a weighted network appear differently in an adjacency matrix?

It would use letters instead of numbers

It would show the actual weight values instead of just 1s and 0s

It would be larger in size

It would only show connected nodes

12. Explain one advantage of using adjacency matrices to represent networks:

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