Fig. 6: Impact of parallel hyperedges on the HCM ensemble.
From: Entropy-based models to randomise real-world hypergraphs
More in detail, trends of \(2\langle {N}_{\parallel }\rangle /L(L-1)=\overline{{p}_{\parallel }}\), i.e., the probability for the generic pair of hyperedges to be parallel and P(N∥ > 0), i.e., the probability of observing at least one pair of parallel hyperedges, are represented as functions of the connectance ρ, respectively, in (a and b). Evaluating the latter in correspondence with the multiple resolution threshold, reading \({p}_{m}^{\,{\mbox{HCM}}\,}\simeq 0.031\) (vertical line), returns 0.493. The dense (sparse) regime is recovered for large (small) values of z. 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.
