Statistics for the hypergraph H.

<p>(a) <i>P</i>(<i>s</i>^<b>H</b>), the distribution of group size <i>s</i>^<b>H</b>, with the distribution in semi-log scale shown in the inset. The two dashed lines in show the range of the tail exponent of <i>P</i>(<i>s</i>^<b>H</b>), namely −3.5 (orange) and −5.0 (magenta). (b) The data collapse of the different broken parts on <i>P</i>(<i>s</i>^<b>H</b>) after re-scaling, in which </p><p></p><p></p><p></p><p><mi>s</mi><mi>c</mi>H</p><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><p><mi>s</mi>H</p><mo>−</mo><p><mi>s</mi></p><p><mi>m</mi><mi>i</mi><mi>n</mi></p>H<p></p><mo stretchy="false">)</mo><mo>/</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><p><mi>s</mi></p><p><mi>m</mi><mi>a</mi><mi>x</mi></p>H<p></p><mo>−</mo><p><mi>s</mi></p><p><mi>m</mi><mi>i</mi><mi>n</mi></p>H<p></p><mo stretchy="false">)</mo><p></p><p></p><p></p>, here <p></p><p></p><p></p><p><mi>s</mi></p><p><mi>m</mi><mi>i</mi><mi>n</mi></p>H<p></p><p></p><p></p><p></p> and <p></p><p></p><p></p><p><mi>s</mi></p><p><mi>m</mi><mi>a</mi><mi>x</mi></p>H<p></p><p></p><p></p><p></p> respectively are the minimum and maximum value of <i>s</i>^<b>H</b> in each section, and <i>P</i>_<i>c</i>(<i>s</i>^<b>H</b>) is the corresponding re-scaled probability. (c) The average (pink) and the standard deviation (grey) of group size given specific date of establishment, and the inset shows the scaling relationship between total of groups and total of users at each date. (d) The distribution <i>P</i>(<i>k</i>^<b>H</b>) of the number of joined group by individual users. <i>P</i>(<i>k</i>^<b>H</b>) for male and female users are shown in the inset. The pink lines correspond to power-law fits with exponent −3.82.<p>