Fig. 9: Scatter plots between the empirical and the expected values for the email-Enron dataset.
From: Entropy-based models to randomise real-world hypergraphs
More in detail, {σi} vs. \(\{{\langle {\sigma }_{i}\rangle }_{{{\rm{HCM}}}}\}\) (a), {κi} vs. \(\{{\langle {\kappa }_{i}\rangle }_{{{\rm{HCM}}}}\}\) (b), {Yi} vs. \({\langle \left\{\right.{Y}_{i}\rangle }_{{{\rm{HCM}}}}\left\}\right.\) (c), and {CECi} vs. \(\{{\langle {{{\rm{CEC}}}}_{i}\rangle }_{{{\rm{HCM}}}}\}\) (d). The HCM overestimates the extent to which any two nodes overlap, as well as the CEC; the disparity ratio, instead, is underestimated by it. These results can be understood by considering that the HCM just constrains the degree sequences, hence inducing an ensemble where connections are ‘distributed'' more evenly than observed.
