Problem
1. Prove that in any simple graph, there are always an even number of vertices with odd vertex degree.
2. Implement a simple version of the PageRank algorithm, and test it on your favorite network. Which vertices get highlighted as most central?
3. For a data set with points at positions (4, 10), (7, 10) (4, 8), (6, 8), (3, 4), (2, 2), (5, 2), (9, 3), (12, 3), (11, 4), (10, 5), and (12, 6), show the clustering that results from
(a) Single-linkage clustering
(b) Average-linkage clustering
(c) Furthest-neighbor (complete linkage) clustering.