# SybilHP: Sybil Detection in Directed Social Networks with Adaptive Homophily Prediction
## 5 Experiment
### General Robustness Evaluation  
We first briefly evaluate the robustness of SybilHP under different conditions including attack edges density, Sybil community scales, and labeling with noises on the Synthesized Pokec dataset.  
Impact of attack edges: We add different numbers of unidirectional attack edges and bidirectional edges (compromised edges) in a ratio of 2:1. Table 3 shows the accuracy decay as the number of attacking edges increases. We found no distinct performance  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Datasets** & **\# Users** & **\# Edges** & **\# Sybils** & **\# Benign** & \(|L_{\mathbf{s}}|\) & \(|L_{\mathbf{b}}|\) \\ \hline Synthesized Pokec & 20,000 & 182,130 & 10,000 & 10,000 & 100 & 100 \\ Twitter & 269,640 & 6,818,501 & 91,263 & 178,377 & 9000 & 17,000 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Overview of the datasets.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Methods** & **Parameter Settings** \\ \hline SybilBelief [16] & \(w=0.9\), \(\theta=0.9\) \\ SybilSCAR [17] & \(w=0.6(\hat{w}=0.1)\), \(\theta=0.6\) \\ GANG [20] & \(w=0.51(\hat{w}=0.01)\), \(\theta=0.9\) \\ GANG\_basic [20] & \(w=0.63(\hat{w}=0.13)\), \(\theta=0.9\) \\ SybilHP & \(\overleftarrow{w}=0.99\), \(\overrightarrow{w_{s}}=0.77\), \(\overrightarrow{w_{b}}=0.97\), \(\overleftarrow{w_{b}}=0.73\), \(\overleftarrow{w_{s}}=0.95\), \(\theta=0.9\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Overview of the parameter settings.  
difference between these homophily-inference-based methods. As the synthesized dataset does not reflect the behavioral preferences of real-world users and Sybil users, the proposed algorithm has only a slight advantage on this dataset, which could be attributed to the additional parameters.  
Impact of Sybil community scale: To be more realistic, we split the Sybil region to form several smaller communities to simulate the scenario when multiple Sybil clusters launch attacks on a benign user community, as shown in Figure 7, where (a), (b), and (c) correspond to one, two, and three Sybil clusters attacking the benign region, respectively. Then, the detection performance of SybilHP is examined. Specifically, we partition the Sybil region by obtaining a certain number of neighboring nodes that constitute the community through a BFS traversal starting at a certain point.  
It can be seen that the total number of Sybil communities increases as the number of individual community nodes decreases, which is similar to the real-world scenario in which Sybil is controlled by different organizations and individuals. We did not change the edges between Sybil and benign regions nor the training set, and the detection performance of SybilHP is shown in Figure 8. It can be seen that the size of the Sybil cluster has almost no impact on the performance of our method. Note, however, that this assumes that nodes in the training set are present in each Sybil cluster.  
Figure 8: Robustness against attacks from different number/scale of Sybil clusters.  
Figure 7: An abridged view of the simulated attack of multiple Sybil clusters.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods 1** & **1K/0.5K** & **2K/1K** & **3K/1.5K** & **4K/2K** & **5K/2.5K** \\ \hline SybilBelief [16] & **0.975** & 0.968 & 0.936 & 0.92 & 0.88 \\ SybilSCAR [17] & 0.971 & 0.965 & 0.932 & **0.923** & **0.881** \\ GANC [20] & 0.973 & 0.959 & 0.929 & 0.92 & 0.87 \\ SybilHP & **0.975** & **0.969** & **0.938** & 0.918 & 0.878 \\ \hline \hline \end{tabular} 1  
\end{table}
Table 3: The classification accuracy under different numbers of attack edges.  
Impact of label noises:In the case of a partially mislabeled training set, LBP-based methods have inherent robustness against label noise. Figure 9 shows the influences of different percentages of false labels on the recall rate for Sybil. We found that SybilBelief and SybilHP showed stronger robustness against label noises compared to SybilSCAR and GANG, which could be due to their nonlinearity.