Forwarding dynamics in a direct follower network.

<p>The figure in the left shows a simple direct follower network of root user 0. When user 0 posts a message, all of his followers will be exposed to this message once (the numbers in braces). In the second step, user 1 forwards this message (dark colour), all the followers of user 1, which is user 2, 3 and 4 (in the shaded area) are exposed to this message one more time. Then user 7 forwards this message. Same thing happens except that now user 4 has been exposed to the message three times since he follows both user 1 and user 7.</p

Variance of the medians of <i>p</i>_<i>m</i>/<i>p</i>_<i>s</i> with respect to the level of popularity of messages.

<p>All the ratios of <i>p</i>_<i>m</i>/<i>p</i>_<i>s</i> are mixed together and divided into four intervals according to the level of popularity of messages. Within these 3,225 samples, we omit 21 very large outliers for clear visualization. The level of popularity increases from the 1st interval to the 4th (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140556#sec012" target="_blank">Materials and Methods</a> for details). Boxplots are plotted for the ratios in each interval. The medians of the ratios, which are 4.654, 4.362, 3.898 and 3.100 respectively, decrease slightly as the level of popularity increases.</p

Mathematical symbols used in prediction.

<p>Mathematical symbols used in prediction.</p

The relation between the prediction error and the saturated forwarding number.

<p>The shaded triangular area encloses most points.</p

Statistics calculated by K-S goodness of fit test for each part of data.

<p>Statistics calculated by K-S goodness of fit test for each part of data.</p

Relative prediction errors for 5 networks with their corresponding root users.

<p>These users are the top 5 most active ones in our data.</p

Statistics calculated by <i>Z</i>-test for every two parts of logarithmically transformed data.

<p>Statistics calculated by <i>Z</i>-test for every two parts of logarithmically transformed data.</p

Number of users who forward messages under certain number of exposures.

<p>For the top 10 most active root users, we count the number of their followers who have forwarded their messages under certain number of exposures, respectively. In this figure, we show the median of these counts with respect to exposure number. In order to clearly show the results, the <i>y</i>-axis is transformed into a logarithmic scale. There are no remarkable forwarding activities when exposure number exceeds 5.</p

Schematic diagram of our popularity prediction method.

<p>Schematic diagram of our popularity prediction method.</p

<i>p</i>-values calculated by permutation test for every two parts of data.

<p>Re-sampling is repeated 10,000 times for each <i>p</i>-value.</p><p><i>p</i>-values calculated by permutation test for every two parts of data.</p