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The question here asks you to create a graph to represent friendship connections between you and a few friends, suggesting a group size of up to six or eight people. In this graph:

1. **Vertices**: Each person, including you, is represented as a vertex (or node) in the graph.
2. **Edges**: Draw an edge (a line) between any two vertices that represent friends.

To complete the task, you can:

1. List yourself and up to seven friends (choose six or eight people in total).
2. Draw a circle with labeled points for each person.
3. Draw a line between any two people who are friends.

This will produce a **friendship graph** or **social network graph**, visualizing who is connected with whom.

Would you like further guidance on how to set up or analyze this type of graph?

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Here are five follow-up questions to deepen understanding:

1. How does the structure of a friendship graph change if everyone is friends with everyone else?
2. What if there are two separate groups in the friend circle who are only friends within their own group?
3. How would adding or removing a friend change the graph?
4. What would the graph look like if you were friends with everyone, but not all friends knew each other?
5. How might this graph change if you could also show friendships of different strengths?

**Tip:** Friendship graphs can be used to model social relationships, and understanding them helps in analyzing network connectivity and clustering.

Create a graph to model your friendship connections with up to six or eight friends. You and your friends are the vertices, with an edge between any two who are friends.

Learn how to create a graph that models friendship connections among a group of up to eight people. Understand vertices and edges in graph theory through a social network example. Suitable for students in Grades 9-12.

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