Fig. 4: Impact of isolated hyperedges on the RHM ensemble.
From: Entropy-based models to randomise real-world hypergraphs
More in detail, trends of 〈N0〉/L = p0, 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 represented as functions of p, respectively in (a–c). Evaluating the first two in correspondence of \({p}_{p}^{\,{\mbox{RHM}}}={h}_{p}^{{\mbox{RHM}}\,}/N=1/\sqrt{NL}\simeq 0.002\) (vertical line) returns, respectively, the values \({e}^{({e}^{-s}-1)/s}\simeq 0.631\) 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 RHM) and is accompanied by the corresponding 95% confidence interval.
