Figure 1.
Examples of undirected (A,B) and directed (C,D) hypergraphs arising in the context of biological networks analysis.
Detailed explanations are given in the text.
Figure 2.
Generating a hypergraph null model by rewiring.
Choose two distinct hyperedges and two different vertices contained in either of the two. Then swap them. Clearly this operation keeps both degree distributions fixed. After a certain number of iterations, the thus-generated Markov chain produces independent samples of the underlying random hypergraph with given degree distributions. In the figure, this is illustrated using the in-this-case simpler-to-visualize bipartite version. The gray double-arrows indicate edges to be swapped. Each of the three swaps, (A,H2)–(C,H3), (B,H1)–(E,H3), and (B,H3)–(D,H1), does not change the vertex and edge degrees. Significance analysis of the CORUM protein complex hypergraph was done in [44] using this idea.