📖 Key Terms and Definitions

A network is a collection of objects (called vertices or nodes) that are connected to each other by links (called edges). Networks help us understand and visualize relationships between different elements.

Example: A social media platform like Instagram is a network where each person is a vertex, and friendships/follows are the edges connecting them.

A vertex is a point or node in a network. It represents an individual object, person, place, or thing that can be connected to other vertices.

Example: In a transport network, each city (like Sydney, Melbourne, Brisbane) would be a vertex.

An edge is a connection or link between two vertices. It shows that there is some kind of relationship or pathway between the connected vertices.

Example: In a transport network, a direct flight route between Sydney and Melbourne would be an edge connecting these two city vertices.

The degree of a vertex is the number of edges connected to that particular vertex. It tells us how many direct connections that vertex has.

Example: If Brisbane has direct flights to Sydney, Melbourne, and Perth, then Brisbane's degree is 3.

Consider this simple network of Australian cities:

Network: Sydney connects to Melbourne and Brisbane. Melbourne connects to Sydney and Adelaide. Brisbane connects to Sydney only. Adelaide connects to Melbourne only.

Step 1: Identify all vertices: Sydney, Melbourne, Brisbane, Adelaide

Step 2: Count edges for each vertex:

• Sydney: connected to Melbourne and Brisbane = degree 2

• Melbourne: connected to Sydney and Adelaide = degree 2

• Brisbane: connected to Sydney only = degree 1

• Adelaide: connected to Melbourne only = degree 1

Hint: Each edge connects two vertices, so count carefully to avoid double-counting!

📚 Part 1: Network Terminology and Identification

(Imagine a simple network with 5 vertices connected by edges)

🌐 Part 2: Real-Life Networks

a) What do the vertices represent? ________________________

b) What do the edges represent? ________________________

c) If Brisbane has direct flights to Sydney, Melbourne, and Perth, what is the degree of the Brisbane vertex? ______

🎨 Part 3: Design Your Own Network

a) List your 5 vertices (cities): _______________________________________________

b) How many edges did you draw? ______

c) Which city has the highest degree? _________________ What is its degree? ______

d) Which city has the lowest degree? _________________ What is its degree? ______