# Spam Classification Based on Signed Network Analysis
## 3 A Primer on Social Psychological Theories for Signed Networks
### Coping with Unsigned Networks
#### 4.1.1 PageRank Analysis  
PageRank, which is a way to measure the importance of a node, has been considered one of the most widely used node influence measurement indices [13,34,35]. In this analysis, we find out whether there exists a correlation between the PageRank score of a node and its edge types through both node-level analysis and edge-level analysis. In the node-level analysis, for all nodes, we measure the ratio of edge types connected to each node. For example, in the example of Figure 3, Node A is connected to three positive edges, two of which are incoming edges and the other is an outgoing edge. Therefore, the ratio of positive incoming edges of Node A is 2/3. Similarly, for the negative edges, the ratio of negative incoming edges of Node A is 1/2. Note that the ratio values for positive edges and negative edges are calculated separately.  
\begin{table}
\begin{tabular}{c c} \hline  & **Twitter** \\ \hline
**The number of users** & 54,981,152 \\
**The number of spammers** & 41,352 \\
**The number of following links** & 1,963,263,821 \\ \hline \end{tabular}
\end{table}
Table 1: Statistics of the Twitter dataset.  
\begin{table}
\begin{tabular}{c c} \hline  & **Epinions** \\ \hline
**The number of nodes** & 131,828 \\
**The number of edges** & 841,372 \\
**The ratio of positive edges** & 85\% \\
**The ratio of negative edges** & 15\% \\ \hline \end{tabular}
\end{table}
Table 2: Statistics of the Epinions dataset.  
Figure 4 shows the measurement results. From Figure 4a, we can see that high ratio values of positive incoming edges are observed more in nodes with high PageRank scores than in those with low PageRank scores. In the case of negative edges (Figure 4b), though the result is less pronounced than in the case of positive edges (Figure 4a), we can see that nodes with high PageRank scores have more outgoing edges. A similar result is observed in average PageRank measurements in Figure 4c; for positive edges, the PageRank score of the source node is lower than of that of the destination node, and vice versa for negative edges.  
In the edge-level analysis, we focus on the difference of PageRank scores between the edge initiator and the edge destination. Table 3 shows a breakdown of the number of edges according to the difference of PageRank scores. For each edge, the difference, \(d\), is computed by subtracting the PageRank score of the destination node from that of the source node. As can be seen from the table, the higher the destination PageRank score is than the source PageRank score (i.e., \(d<0\)),  
Figure 4: PageRank measurements at the node level. Nodes with higher PageRank scores have more positive incoming edges and negative outgoing edges than those with lower scores.  
Figure 3: An example of signed networks. A node may be connected to several nodes through different types of edges.  
the more positive edges are observed (64.67%). In the opposite case (i.e., \(d>0\)), more negative edges are observed (64.99%). The above observations are consistent with the social status theory, where a lower-status node (i.e., lower PageRank score) is more likely to give a positive sign to a higher-status node (i.e., higher PageRank score).