Power-Law Properties of Human View and Reply Behavior in Online Society

<table>The power-law relationship between <svg height="11.375" id="M42" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 12.7375 11.375" width="12.7375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D449"></use></g>
</svg> and <svg height="11.3125" id="M43" style="vertical-align:-0.1092pt" version="1.1" viewbox="0 0 11.075 11.3125" width="11.075" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D445"></use></g>
</svg>, where (a) sub-forum A, the slope <svg height="15.35" id="M44" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 56.412498 15.35" width="56.412498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5
t0.5 -143.5h2q155 193 155 297q0 26 -12 47q-5 8 -5 15q0 16 12.5 27t29.5 11q21 0 34 -21t13 -55z" id="x1D6FE"></path></g><g transform="matrix(.017,-0,0,-.017,13.288,10.862)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,27.991,10.862)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,36.151,10.862)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,40.027,10.862)"><use xlink:href="#x37"></use></g><g transform="matrix(.017,-0,0,-.017,48.186,10.862)"><use xlink:href="#x37"></use></g>
</svg>, (b) sub-forum B, the slope <svg height="15.35" id="M45" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 56.412498 15.35" width="56.412498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><use xlink:href="#x1D6FE"></use></g><g transform="matrix(.017,-0,0,-.017,13.288,10.862)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,27.991,10.862)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,36.151,10.862)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,40.027,10.862)"><use xlink:href="#x38"></use></g><g transform="matrix(.017,-0,0,-.017,48.186,10.862)"><use xlink:href="#x39"></use></g>
</svg>, (c) sub-forum C, the slope <svg height="15.35" id="M46" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 56.412498 15.35" width="56.412498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><use xlink:href="#x1D6FE"></use></g><g transform="matrix(.017,-0,0,-.017,13.288,10.862)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,27.991,10.862)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,36.151,10.862)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,40.027,10.862)"><use xlink:href="#x38"></use></g><g transform="matrix(.017,-0,0,-.017,48.186,10.862)"><use xlink:href="#x35"></use></g>
</svg>, (d) sub-forum D, the slope <svg height="15.35" id="M47" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 56.412498 15.35" width="56.412498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><use xlink:href="#x1D6FE"></use></g><g transform="matrix(.017,-0,0,-.017,13.288,10.862)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,27.991,10.862)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,36.151,10.862)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,40.027,10.862)"><use xlink:href="#x39"></use></g><g transform="matrix(.017,-0,0,-.017,48.186,10.862)"><use xlink:href="#x30"></use></g>
</svg>.</table>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Power-Law Properties of Human View and Reply Behavior in Online Society 