Fig. 4: Higher-order interactions decrease degree heterogeneity in random hypergraphs.

The degree heterogeneity (measured by h⁽¹⁾ and h⁽²⁾) is stronger in the first-order Laplacian L⁽¹⁾ than in the second-order Laplacian L⁽²⁾, and the difference increases with system size n. The theoretical lower bound of \(\frac{{h}^{(1)}}{{h}^{(2)}}\) is given by \(\frac{\sqrt{n}}{2}\) and is independent of p. The simulation results are obtained from random hypergraphs with different sizes n, using 500 samples for each n. The connection probabilities are set to p = p_△ = 0.1.