2. Modeling as Graphs Alice is throwing a party and invites her friends Bob, Claire, and Dan. Bob is only friends with Alice. Dan and Claire are friends. Dan brings along his friend Eve to the party, and Eve is not friends with Alice, Bob, or Claire. (a) Model the friendship relationships as a graph. Party-goers are vertices, and edges are friendships. For sim plicity, you can label the vertices by A,B,C,D, and E, in which A denotes Alice, B denotes Bob and so on. (b) write down the adjacency matrix of the above graph. ( use A 0, B 1, etc.) (c) Write down the adjacency list of the above graph. ( use A 0, B1, etc.) (d) Which vertex has the highest degree (give the person's name)? Which has the lowest? What are the degrees of these vertices? What does vertex degree tell you about the person that vertex represents