Ut topology is not the only means of information U0126-EtOH price diffusion in social networks as it is in web networks. This paper decomposes the influential effects of a particular user into two parts: direct influence, which is triggered by a retweet action, and indirect influence, which is caused by the actions of others, without necessarily involving a following relationship. In total, users generate an enormous number of tweets everyday on social media. Topicmixed tweets propagate through the same network, and these various tweets contain the topicrelated information. Faced with this flood of information, information seekers [7] are eager to follow only the most valuable users for a given topic. Actually, because sharing the same network structure, it is hard to distinguish different topics from the same information propagation. Discovering topic-dependent influential leaders enables user find the topic-related posters. On the other hand, Social network sites show new users a list of topics from which they can choose the ones they are most interested in following. Then, the most influential user for this topic will be recommended to the new user. Therefore, this “cold start” problem [8] could be well solved by recommending topic-related influential users. Importantly, influential users for one topic may fail to have the same influence for other topics, which means users play different roles in different topics [9]. Therefore, influence is topic-dependent, making it necessary to discover the topic-dependent influential leaders. In this paper, we propose a novel influential model called the multi-topic influence diffusion (MTID) model to discover topic-related influential leaders. Specifically, the influence of these users in our model consists of both direct and indirect influence. The direct influence follows the information propagation trace along the links. Meanwhile, users can retweet tweets posted by people they are not following, giving the original posters further indirect influence. Notice that both types of influence are related to different topics. Based on MTID, we further propose a topic-dependent rank algorithm, namely TD-Rank. Different from setting one ground node to make the network strongly connected, as in LeaderRank [10] [11], we treat ground nodes asPLOS ONE | DOI:10.1371/journal.pone.0158855 July 14,2 /Discover Influential Leadersthe different topic pools of original tweets to construct a topical view of the whole network. Connecting all the nodes with each ground node hence represents a one-topic view of the network. This view is strongly connected and, thus, has the same properties as LeaderRank. Moreover, the transition probability in our model is extracted from traces of tweet action including both posting of the original tweet and retweeting others’ tweets. This approach has been shown to be helpful in finding influential users [12]. We further experimentally demonstrate that our proposed ranking algorithm extracts nontrivial nodes as influential nodes in various topics on the large-scale Weibo network.Related workGenerally, discovering influential leaders is related to two research topics. The first is measuring the maximization of influence. Influence maximization aims to find a set of seed users that influence a large number of other users. This problem was first RG7666 dose studied by Domingos and Richardson from an algorithmic perspective [13]. Then, Kempe et al. [1] formulated the problem as a combinatorial discrete optimization.Ut topology is not the only means of information diffusion in social networks as it is in web networks. This paper decomposes the influential effects of a particular user into two parts: direct influence, which is triggered by a retweet action, and indirect influence, which is caused by the actions of others, without necessarily involving a following relationship. In total, users generate an enormous number of tweets everyday on social media. Topicmixed tweets propagate through the same network, and these various tweets contain the topicrelated information. Faced with this flood of information, information seekers [7] are eager to follow only the most valuable users for a given topic. Actually, because sharing the same network structure, it is hard to distinguish different topics from the same information propagation. Discovering topic-dependent influential leaders enables user find the topic-related posters. On the other hand, Social network sites show new users a list of topics from which they can choose the ones they are most interested in following. Then, the most influential user for this topic will be recommended to the new user. Therefore, this “cold start” problem [8] could be well solved by recommending topic-related influential users. Importantly, influential users for one topic may fail to have the same influence for other topics, which means users play different roles in different topics [9]. Therefore, influence is topic-dependent, making it necessary to discover the topic-dependent influential leaders. In this paper, we propose a novel influential model called the multi-topic influence diffusion (MTID) model to discover topic-related influential leaders. Specifically, the influence of these users in our model consists of both direct and indirect influence. The direct influence follows the information propagation trace along the links. Meanwhile, users can retweet tweets posted by people they are not following, giving the original posters further indirect influence. Notice that both types of influence are related to different topics. Based on MTID, we further propose a topic-dependent rank algorithm, namely TD-Rank. Different from setting one ground node to make the network strongly connected, as in LeaderRank [10] [11], we treat ground nodes asPLOS ONE | DOI:10.1371/journal.pone.0158855 July 14,2 /Discover Influential Leadersthe different topic pools of original tweets to construct a topical view of the whole network. Connecting all the nodes with each ground node hence represents a one-topic view of the network. This view is strongly connected and, thus, has the same properties as LeaderRank. Moreover, the transition probability in our model is extracted from traces of tweet action including both posting of the original tweet and retweeting others’ tweets. This approach has been shown to be helpful in finding influential users [12]. We further experimentally demonstrate that our proposed ranking algorithm extracts nontrivial nodes as influential nodes in various topics on the large-scale Weibo network.Related workGenerally, discovering influential leaders is related to two research topics. The first is measuring the maximization of influence. Influence maximization aims to find a set of seed users that influence a large number of other users. This problem was first studied by Domingos and Richardson from an algorithmic perspective [13]. Then, Kempe et al. [1] formulated the problem as a combinatorial discrete optimization.