Figure 1.
An illustration of the ground node and the LeaderRank algorithm.
The social network consists of six users and 12 directed links. The final ranking scores are labeled next to the corresponding users.
Table 1.
Top 20 users ranked by the three approaches.
Figure 2.
The number of fans of a user in descending order of the user rank by LeaderRank.
The size of the solid circle is proportional to the value of , i.e. the average number of time their collected bookmarks are saved by others. Users highlighted with the red circles have a small number of fans but a large value of
. On the contrary, users highlighted with the blue circles have a large number of fans but a small value of
.
Figure 3.
Users (a) cffcoach, (b) pedersoj, (c) kanter and (d) britta, who are ranked respectively at ,
,
and
by LeaderRank, as surrounded by their fans.
The size of circles represents the average number of times their collected bookmarks are saved by others.
Figure 4.
The cumulative number of infected users (including recovered users), , as a function of time, with initial infected to be the users either appear as (a) top-20, (b) top-50, and (c) top-100 by LeaderRank or PageRank (but not both).
As we see from Table 1 in the top-20 case, the initial infected users by LeaderRank are blackbeltjones, regina, zephoria and djakes, while that by PageRank are thetechguy, cffcoach, samoore and kevinrose. Infection probability and return probability is set to 0.15 in PageRank. (d) As a function of
, the quotient of the number of infected users in LeaderRank divided by that of PageRank, expressed as fractional increase.
Figure 5.
The impact on (a) scores and (b) ranking as a function of number of links added and removed.
Inset: (b) the difference in ranking mobility between LeaderRank and PageRank.
Figure 6.
The manipulated rank as obtained by (a) LeaderRank and (b) PageRank, after the addition of fake fans, with
.