Fig 1.
Examples of 3-uniform hypergraphs.
(A) Complete 3-uniform hypergraph with N = 4 nodes. (B) Cyclic 3-uniform hypergraph with N = 8 nodes. (C) Star 3-uniform hypergraph with N = 5 nodes. Each colored oval represents a hyperedge.
Fig 2.
Fixation probability for different hypergraph models under model 1.
We compare the Moran process, which is the baseline, complete 3-uniform hypergraphs, cyclic 3-uniform hypergraphs, and star 3-uniform hypergraphs. (A) N = 4. (B) N = 5. (C) N = 20. (D) N = 200. The insets in (C) and (D) magnify the results for r values smaller than and close to r = 1. In these insets and main panel (B), the results for the complete 3-uniform hypergraph are close to those for the cyclic hypergraph such that the blue lines are almost hidden behind the orange lines. In (A), the two results are exactly the same such that the blue line is completely hidden behind the orange line.
Fig 3.
State transitions in the cyclic 3-uniform hypergraph.
(A) A state with just one node of type A (i.e., i = 1). (B) A state with just one node of type B (i.e., i = N − 1). (C) A state with more than one nodes of each type (i.e., 2 ≤ i ≤ N − 2).
Fig 4.
Fixation probability for different hypergraph models under model 2.
We compare the Moran process, which is the baseline, complete 3-uniform hypergraphs, cyclic 3-uniform hypergraphs, and star 3-uniform hypergraphs. (A) N = 4. (B) N = 5. (C) N = 20. (D) N = 200. In (A), the result for the complete 3-uniform hypergraph is exactly the same as that for the cyclic 3-uniform hypergraph such that the blue line is completely hidden behind the orange line. In (C) and (D), the results for the complete 3-uniform hypergraph (shown by the blue lines) are not identical but close to those for the star hypergraph (shown by the green lines) such that the former are hidden behind the latter.
Fig 5.
Fixation probability for empirical hypergraphs, their one-mode projection, and the randomized hypergraphs.
(A) Corporate. (B) Enron. (C) Senate. (D) High-school. The insets of (B), (C), and (D) magnify the results for r values smaller than and close to r = 1. We estimated the fixation probability at each value of r as the fraction of runs in which fixation of type A is reached. We find that empirical and randomized hypergraphs are suppressors of selection for all the four data sets.