Rank after the addition of v spammers. As result, the diagonal line is the baseline, which indicates the rank is invariant. Vertical shift from the diagonal line corresponds to the change of ranking results. In addition, for ease of visualization, we select the ranking list on topic #1 as an example to show the comparative performance of TwitterRank and TD-Rank. As shown, TD-Rank is the most robust against spammers because the changes in ranking positions are much smaller than those of the other algorithms, and TwitterRank is more robust than PageRank and LeaderRank. Therefore, the results are mainly due to the distinguishing topics. In all, TD-Rank is a better algorithm for creating robust rankings in social network.PLOS ONE | DOI:10.1371/journal.pone.0158855 July 14,9 /Discover Influential LeadersPLOS ONE | DOI:10.1371/journal.pone.0158855 July 14,10 /Discover Influential LeadersFig 3. The topic entropy. (a) Comparison between PageRank, LeaderRank and TD-Rank; (b) Comparison between TD-Rank and TwitterRank on top 10 users. doi:10.1371/journal.pone.0158855.gThe next issue is influence maximization. We first JNJ-54781532 solubility consider two information-diffusing models in previous work [25]. Independent Cascade (IC) Model: This model begins with an initial set of active nodes. The process unfolds in discrete steps. When node v first becomes active in step t, it has a single chance to activate each currently inactive neighbor w based on parameter pv,w. In our experiment, we set the parameter pv,w uniformly to 0.1. Topic Independent Cascade (TIC) Model: This model uses the same process as IC, but its the parameter pv,w is related to topic. Specifically, the probability of diffusion is defined as: pv;w ?T X t?gtv ptv;w?1?Fig 4. The spammer effect on ranking results. (a) PageRank, (b) LeaderRank (c) TwitterRank, (d) TD-Rank. doi:10.1371/journal.pone.0158855.gPLOS ONE | DOI:10.1371/journal.pone.0158855 July 14,11 /Discover Influential LeadersFig 5. Comparison of influence maximization. (a) The results of IC Model. (b) The results of TIC Model. doi:10.1371/journal.pone.0158855.gwhere gtv is the topic probability of user v on topic t, and ptv;w represents the influence strength exerted by user v on w on topic t. We conduct experiments on IC and TIC with the top 10 users in every ranking results consisting of the initial set of active nodes. In addition, the top 10 users in TD-Rank and TwitterRank are also selected from the ranking list of topic #1 as additional experiments. The results are shown in Fig 5. Because it ignores the effects of topic distribution, the IC model is more suitable for a comprehensive ranking algorithm. However, it is worth noting that TD-Rank converges to a stable number faster than the others, which indicates that TD-Rank is more inclined to measure the influence of users on one particular topic with a smaller population. Tenapanor supplier Compared to TIC, TD-Rank and TwitterRank calculate the influence on more users by considering topic effects. In all, this experiment shows the essential value of taking the topic factor into account. We also extracted the number of retweets for several tweets posted by the top 50 users in the whole dataset. Then, we investigated the differences between this true retweet number and the number obtained by TIC. Assuming that the set of tweets posted by user i is denoted by di, we then evaluate the influence-predicting performances of all the algorithms using the mean squared error (MSE) as the evaluation metric: !2 ! N 1X.Rank after the addition of v spammers. As result, the diagonal line is the baseline, which indicates the rank is invariant. Vertical shift from the diagonal line corresponds to the change of ranking results. In addition, for ease of visualization, we select the ranking list on topic #1 as an example to show the comparative performance of TwitterRank and TD-Rank. As shown, TD-Rank is the most robust against spammers because the changes in ranking positions are much smaller than those of the other algorithms, and TwitterRank is more robust than PageRank and LeaderRank. Therefore, the results are mainly due to the distinguishing topics. In all, TD-Rank is a better algorithm for creating robust rankings in social network.PLOS ONE | DOI:10.1371/journal.pone.0158855 July 14,9 /Discover Influential LeadersPLOS ONE | DOI:10.1371/journal.pone.0158855 July 14,10 /Discover Influential LeadersFig 3. The topic entropy. (a) Comparison between PageRank, LeaderRank and TD-Rank; (b) Comparison between TD-Rank and TwitterRank on top 10 users. doi:10.1371/journal.pone.0158855.gThe next issue is influence maximization. We first consider two information-diffusing models in previous work [25]. Independent Cascade (IC) Model: This model begins with an initial set of active nodes. The process unfolds in discrete steps. When node v first becomes active in step t, it has a single chance to activate each currently inactive neighbor w based on parameter pv,w. In our experiment, we set the parameter pv,w uniformly to 0.1. Topic Independent Cascade (TIC) Model: This model uses the same process as IC, but its the parameter pv,w is related to topic. Specifically, the probability of diffusion is defined as: pv;w ?T X t?gtv ptv;w?1?Fig 4. The spammer effect on ranking results. (a) PageRank, (b) LeaderRank (c) TwitterRank, (d) TD-Rank. doi:10.1371/journal.pone.0158855.gPLOS ONE | DOI:10.1371/journal.pone.0158855 July 14,11 /Discover Influential LeadersFig 5. Comparison of influence maximization. (a) The results of IC Model. (b) The results of TIC Model. doi:10.1371/journal.pone.0158855.gwhere gtv is the topic probability of user v on topic t, and ptv;w represents the influence strength exerted by user v on w on topic t. We conduct experiments on IC and TIC with the top 10 users in every ranking results consisting of the initial set of active nodes. In addition, the top 10 users in TD-Rank and TwitterRank are also selected from the ranking list of topic #1 as additional experiments. The results are shown in Fig 5. Because it ignores the effects of topic distribution, the IC model is more suitable for a comprehensive ranking algorithm. However, it is worth noting that TD-Rank converges to a stable number faster than the others, which indicates that TD-Rank is more inclined to measure the influence of users on one particular topic with a smaller population. Compared to TIC, TD-Rank and TwitterRank calculate the influence on more users by considering topic effects. In all, this experiment shows the essential value of taking the topic factor into account. We also extracted the number of retweets for several tweets posted by the top 50 users in the whole dataset. Then, we investigated the differences between this true retweet number and the number obtained by TIC. Assuming that the set of tweets posted by user i is denoted by di, we then evaluate the influence-predicting performances of all the algorithms using the mean squared error (MSE) as the evaluation metric: !2 ! N 1X.