You will be applying graph theory concepts to the context of social networks. Complete the following tasks:

1. Create a graph with 10 vertices where each vertex is labeled with the name of a person in your social network. Include yourself as one of those vertices.
2. State what the edges of your graph represent in this context.
3. Discuss any characteristics you note about the graph you created in part (b). In your discussion, make sure to address the following:

• What are the degrees of each vertex?
• Is it a complete graph?
• Is the graph planar?

1. We refer to the number of steps between two people as thedegree of separationbetween them.

• What is the largest degree of separation from you to any other person in your social network graph?
• What is the largest degree of separation between any two people in your social network graph?

1. Research about the maximum degrees of separation that has been hypothesized between any two people around the world. Discuss how graph theory concepts are involved in this research.