Comparison of the two global hypergraph clustering coefficient measures on random hypergraphs. The x-axis shows the probability p with which a hyperedge with a fixed cardinality is added, and the y-axis shows the value of the global clustering coefficient. Each hypergraph has 30 nodes. Solid and dashed lines correspond to our measure (Eq. 5) and the ERV measure (Eq. 7). Red, blue, green and magenta colors correspond to hyperedge cardinalities 2, 3, 4, and 5, respectively. A completely connected hypergraph has p = 1. Note that for |E| = 2 (red) the two coefficients agree and both degenerate into the standard graph clustering coefficient . Each data point shows the median of 15 replica and the error bar shows the upper and lower quartiles.