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Choose ten of your friends, and make a graph where the edges represent two friends being Facebook friends. (Do not include yourself in the graph). Order your friends alphabetically, and label the vertices v1, v2, ..., v10 respectively.

This will be most interesting if all of your friends know each other. Now, answer the following questions about the graph that you drew.

(a) Find the shortest and longest paths from v1 to v10.
(b) Which vertex has the highest degree?
(c) Find minimum spanning tree, and draw that tree.

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