Fig. 7: Impact of isolated hyperedges on the HCM ensemble.
From: Entropy-based models to randomise real-world hypergraphs
More in detail, trends of \(\langle {N}_{0}\rangle /L=\overline{{p}_{0}}\), i.e., the probability for the generic hyperedge to be isolated in the projection, P(N0 > 0), i.e., the probability of observing at least one, isolated hyperedge in the projection, and ∣LCC∣/N, i.e., the percentage of nodes belonging to the largest connected component (LCC), are repesented as functions of the connectance ρ, respectively, in (a–c). Evaluating the first two in correspondence of \({p}_{p}^{\,{\mbox{HCM}}\,}\simeq 0.001\) (vertical line), returns the values ≃ 0.766 and ≃ 1. The dense (sparse) regime is recovered for large (small) values of p. Each dot represents an average taken over an ensemble of 103 configurations (explicitly sampled from the HCM) and is accompanied by the corresponding 95% confidence interval.
