Fig. 7: Link between reducibility and degree heterogeneity by randomizing.

We focus on the “contact” datasets because they have high reducibility and nestedness. To each dataset (black), we apply three randomizing strategies: the configuration model (green) a node swap (blue), and a random shuffling of hyperedges (red). In each case, we show a the reducibility, b the nestedness measured by the simplicial fraction, c the cross-order degree correlation between orders 1 and 2, and d the degree heterogeneity. Each dot represents one of 20 realizations of each randomizing strategy. Although all randomizing strategies destroy the nestedness, preserving the degree heterogeneity is sufficient to preserve the reducibility.