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Feb 10, 2016 at 19:23 comment added David Eppstein Yes, pagerank is often the first example I give for why students should care about graph algorithms. As for counting spanning trees, it's called the matrix-tree theorem or Kirchoff's theorem; see also en.wikipedia.org/wiki/Kirchhoff%27s_theorem
S Feb 10, 2016 at 3:37 history answered Richard Montgomery CC BY-SA 3.0
S Feb 10, 2016 at 3:37 history made wiki Post Made Community Wiki by Richard Montgomery