Fig. 3. U.S. members of congress (nodes) cosponsoring bills (hyperedges) exhibit certain notions of same-class homophily in terms of political party.

(A) Affinity scores (top row) increase for Democrats but are relatively flat for Republicans. However, after dividing by baselines (middle row), both classes exhibit bowl-shaped ratio scores that nearly satisfy majority homophily (higher-than-baseline affinities for groups where one’s class is the majority) and monotonic homophily (strictly increasing ratio scores for groups where one’s class is in the majority) without ever violating our theoretical impossibility results. For example, for bills with five cosponsors, Democrats exhibit monotonic homophily, and Republicans almost do as well, except for a slight decrease in scores from t = 2 to t = 3 (middle row, leftmost). Similar observations hold for bills of other cosponsorship sizes. (B) Both Republicans (Re) and Democrats (De) almost always exhibit the highest possible MoHI without violating combinatorial limits (e.g., MoHI of k/2 for both parties when k is even). Neither class exhibits majority homophily. However, as group size increases, the MaHI (the number of top affinity scores above baseline) increases. Bold entries correspond to plots for bills with 5, 10, and 15 cosponsors. Our results are also robust to perturbations in the data; we obtain nearly identical plots when averaging scores obtained by repeatedly subsampling hyperedges from the dataset (see the Supplementary Materials).