I've uploaded another handout related to Gomory-Hu trees on the Blackboard site. This is a Chapter from the classical book Flows in Networks by Ford and Fulkerson. In it, you'll find some background and motivation for cut- and flow-equivalent trees.
It also contains a worked-out example of the algorithm so you can make sure you understand it.
While scanning this today, I realized that we've pretty much covered most of the topics discussed in this book: maximum s-t flows, minimum s-t cuts, minimum-cost flows and circulations, and now Gomory-Hu trees. Of course, many details have changed in the almost 50 years since the book was written. For example neither Edmonds-Karp nor Goldberg-Tarjan algorithms were known as such then. The minimum mean cycle paper is also more than 15 years younger than the book. Also, there are many details and a few different viewpoints that the book covers that we haven't gotten to yet.
After we wrap up Gomory-Hu trees, we'll proceed to matchings and then some linear and integer programming to expose the duality between some pairs of problems that we've studied already.
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