Problem Statement

Shared context — identical in all four questions in this set. The scenario and artifacts below are exactly the same across all four questions; only the Question section changes. If you have already read them in another question, skip straight to Question. Your university’s annual hackathon has 120 student teams. There are not enough judges to score each team individually, so the organisers use pairwise comparisons : each judge is asked to look at a handful of pairs and decide which team is stronger. After the round, you have ~600 comparisons in the form (judge_id, team_a, team_b, winner) . Some judges only saw two teams; others saw eight. Judges sometimes disagree (A>B and B>A from different judges). The organisers want a final ranking of the 120 teams to publish at the closing ceremony in two hours. Question Model the comparison data as a graph. What do nodes, edges, and edge weights mean? What graph property determines whether a total ranking is even meaningful here? Provided A