# SybilHP: Sybil Detection in Directed Social Networks with Adaptive Homophily Prediction
## 2 Related Work  
Both random-walk-based methods and LBP-based methods start from some labeled nodes to predict the unknown labels by semi-supervised learning. The basic idea of random-walk-based methods is that random walks starting from benign nodes tend to reach other benign nodes quickly, while it is difficult for Sybil to reach a benign node in a short walk. From this intuition, SybilGuard [10] and SybilLimit [11] have spawned many works, including SmartWalk [33], Sybillfer [12], SybilRank [9], SybilWalk [19], and Integro [15]. However, note that the training set for these methods should either consist of benign users or Sybil users but not both.  
On another front, leveraging both labeled Sybil and benign nodes, LBP-based methods model the joint distribution over each node's label with Markov random fields and then use the LBP algorithm to iteratively estimate posterior probability distributions for unknown labels. Stemming from the seminal SybilBelief [16], SybilSCAR [17] integrates LBP-based and RW-based methods into a unified framework and further simplifies the local update rule for posterior estimation, which largely enhances the detection efficiency of LBP-based methods. SybilFuse [18] incorporates local graph attributes to better estimate the node priors by pre-trained classifiers and then uses LBP to compute the posteriors. [PERSON] et al. [24] first showed that existing graph-based Sybil-detection methods can be interpreted in a unified framework of low-pass filtering, and then they proposed SybilHeat.  
However, for directed edges, the methods mentioned above either prune the one-way edges and retain those bidirectional ones, or they directly treat all edges as undirected, causing under-use of the original edge information. Worse still, \"sparse connection\" or \"homophily assumption\" requires a significant structural gap between Sybil and benign communities. However, such a structural gap in the directed social graph can be particularly obscure because the one-way linkage is much easier to achieve, and Sybils can link to benign users as many as they want. [PERSON] [20] adapted LBP for a directed graph by incorporating the one-way edge scenario into the edge-potential design and further derived a scalable and convergent matrix form. However, the use of a global edge weight still limits its modeling fidelity.  
Based on social graph data, recent works have tended to incorporate various side information. For example, SybilHunter [23] provides a hybrid graph-based Sybil-detection approach by aggregating user social behavior patterns. [PERSON] et al. [26] first applied graph convolutional networks to social robot detection. The use of GCN makes it possible to perform end-to-end learning using both node attribute information and node structure information. TrustGCN [27] used a \"friend request\" graph and, by combining social-graph-based defenses and graph neural networks, improved the robustness of adversarial attacks.  
BotRGCN [28] and SATAR [29] applied graph convolutional networks on a Twitter follower-followee graph with multi-modal user semantics, properties, and neighborhood information. Improved CGAN [34] manages to extend imbalanced data sets before applying training classifiers to improve the detection accuracy of social bots. RoSGAS [35] is a novel reinforced and self-supervised GNN architecture search framework that adaptively pinpoints the most suitable multi-hop neighborhood and the number of layers in the GNN architecture for social bot detection. However, as the neural network-based models become more complex, the cost of training and deploying the models increases, which limits their scalability and portability.