Table 1 Properties of empirical datasets and their simpliciality. \(|V|\), \(|E|\), \(\langle k\rangle \), \(\langle s\rangle \), \(\sigma _{\mathrm{SF}}\), \(\sigma _{\mathrm{ES}}\), and \(\sigma _{\mathrm{FES}}\) denote the number of nodes, the number of hyperedges, the mean degree, the mean edge size, the simplicial fraction (SF), edit simpliciality (ES), and the face edit simpliciality (FES), respectively
Dataset | |V| | |E| | 〈k〉 | 〈s〉 | \(\sigma _{\mathrm{SF}}\) | \(\sigma _{\mathrm{ES}}\) | \(\sigma _{\mathrm{FES}}\) |
|---|---|---|---|---|---|---|---|
Proximity datasets | |||||||
contact-primary-school | 242 | 12,704 | 52.50 | 2.42 | 0.85 | 0.92 | 0.94 |
contact-high-school | 327 | 7,818 | 23.91 | 2.33 | 0.81 | 0.93 | 0.92 |
hospital-lyon | 75 | 1,824 | 24.32 | 2.43 | 0.91 | 0.95 | 0.97 |
Email datasets | |||||||
email-enron | 143 | 1,442 | 10.08 | 2.97 | 0.31 | 0.05 | 0.50 |
email-eu | 967 | 23,729 | 24.54 | 3.12 | 0.32 | 0.05 | 0.52 |
Biological datasets | |||||||
diseasome | 516 | 314 | 0.61 | 3.00 | 0.00 | 0.05 | 0.04 |
disgenenet | 1,982 | 760 | 0.38 | 5.14 | 0.00 | 0.00 | 0.01 |
ndc-substances | 2,740 | 4,754 | 1.74 | 5.16 | 0.02 | 0.01 | 0.07 |
Other | |||||||
congress-bills | 1,715 | 58,788 | 34.28 | 4.95 | 0.03 | 0.01 | 0.10 |
tags-ask-ubuntu | 3,021 | 145,053 | 48.01 | 3.43 | 0.15 | 0.25 | 0.46 |