There is a huge amount of information generated in online social networks, which is filled with a lot of rumors. The spread of a rumor often leads to the generation of a causal related rumor, and when users believe the first kind of rumor, the probability of being influenced by another causal related rumor is larger. Therefore, the influence probability will change with the process of rumor spreading. In this paper, we design the Causal Rumors Enhance Cascade ($CREC$) model to describe the spreading process of causal related rumors. Then we attempt to select a set of seed users that minimizes the number of users expected to be influenced by rumors, which we call the Causal Related Rumors Controlling (CRRC) problem. The main challenges of this problem are that the influence probability is constantly changing during the spread process, so the reverse sampling technique cannot be used, and the greedy mechanism is not suitable for massive-scale datasets. For the sake of overcoming these challenges and solving the problem, we put forward the Degree Trigonometric Metrology (DTM) algorithm, which uses the property of three-directed circles in the directed network to select seed nodes. Finally, experiments on three massive-scale datasets show that our algorithm outperforms the other algorithms.

It is undeniable that rumors abound on online social networks and rumors can cause many disastrous consequences. Effective controlling of rumors is of great significance in social networks. However, the existing research only selects boosting users who are more likely to adopt the truth or select blocking users to terminate the spread of rumors. The former tends to correct the rumor after the spread is over but with high controlling cost, while the latter blocks the rumor without considering the truth transmission. In this article, we focus on how to select boosting–blocking users to control rumors when the rumor and truth are spreading together. We propose a boosting-truth blocking-rumor cascade (BTBRC) model. Under this model, given the rumor seed set and truth seed set, the boosting rumor controlling (BRC) problem aims to find a boosting–blocking seed set with$k$users such that the number of users influenced by the truth can be maximized. In order to solve it, we design a multihop neighbor boosting (MHNB) algorithm, which can get effective results with a data-parameter-dependent approximation ratio. Based on the above model, we also propose a positive boosting-truth blocking-rumor cascade (PBTBRC) model and design a connected multihop neighbor boosting (CMHNB) algorithm to solve the connected positive boosting rumor controlling (CPBRC) problem that requires a seed set to be connected under this model. Finally, extensive theoretical analysis and experimental results show the superiority of our algorithms over other comparison methods.