Figure 1.

(left) A hypergraph $H=(V,E)$ with five nodes and three hyperedges; (center) The weighted clique expansion ${\left[H\right]}_2^w$ associated with H (the edge weight, depicted on each edge, corresponds to the number of hyperedges containing both endpoints); (right) The bipartite incidence graph $I\left(H\right)$ associated with H (the five nodes appear on the left and the three hyperedges appear on the right).