Fig. 4: The process to construct the n-reduced graph.
From: Unveiling the role of higher-order interactions via stepwise reduction
a shows the original structure, b illustrates the 3-reduction process, and c displays the reorganized structure. This hypergraph contains eight nodes and seven hyperedges. Among them, the orders of e2, e3, and e5 are 2, the orders of e1, e4 and e6 are 3, and the order of e7 is 4. When n = 3, hyperedge e7 is decomposed into all combinations of its nodes, say {v1, v2, v3}, {v1, v2, v5}, {v1, v3, v5}, and {v2, v3, v5}.
