# Identifying Influential Nodes of Complex Networks Based on Trust-Value
## 3 Experiments and Discussion
### Analysis of SIR Spreading Model  
In the SIR propagation verification, since the propagation ability of a node is more representative in the initial propagation phase [13], in this paper, the seed node only propagates for 10 steps (\(t=10\)) instead of the whole infection reaching a steady state. First, in each iteration, the infected nodes infect their neighbor nodes with a probability of 0.3 and return to recovery state with a probability of 1, which means \(\beta=0.3,\gamma=1\). The TPR algorithm was compared with the DC, BC, PageRank, and HITS algorithms. The statistical results between the influence values of the nodes calculated by these algorithms and the nodes' propagation ability by the SIR model are shown in Figure 6. In general, the stronger the positive correlation of the scatter graph, the closer the algorithm's results are to the SIR model and the more appropriate the algorithm. Figure 5: Two small-scale networks. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Kite**} & \multicolumn{6}{c}{**Karate**} \\ \hline
**Sort** & **DC** & **BC** & **PageRank** & **HITS** & **TPR** & **sort** & **DC** & **BC** & **PageRank** & **HITS** & **TPR** \\ \hline
1 & 7 & 3 & 7 & 7 & 7 & 1 & 34 & 1 & 34 & 34 & 1 \\
2 & 4 & 4 & 4 & 4 & 4 & 2 & 1 & 34 & 1 & 1 & 34 \\
3 & 5 & 5 & 5 & 5 & 5 & 3 & 33 & 33 & 33 & 33 \\  
In the Email network (Figure 6a), DC, PageRank, HITS, and TPR algorithms can accurately reflect that the influence and SIR propagation ability of nodes are positively related. The distributions of nodes in DC, PageRank, and TPR algorithms are concentrated, whereas the distribution of the nodes in BC is more dispersed overall. In the Euoroad network (Figure 6b), each algorithm exhibits positive correlation characteristics. This feature is more obvious in TPR and PageRank, whereas DC cannot distinguish nodes with the same influence. BC performed poorly and the nodes gathered on the left side of the horizontal axis. In the HITS algorithm, some nodes with high propagation ability in the SIR model have low HITS values. The DC, PageRank, HITS, and TPR algorithms performed similarly in the Protein network (Figure 6c), and the distribution of nodes in the BC algorithm was relatively scattered. These algorithms performed similarly on the Euoroad and Power Grid networks (Figure 6d). From the above experimental results, in the Email, Euoroad, and Protein networks, the centrality value calculated by the TPR was more linearly consistent with the propagation ability obtained by the SIR model; that is, the nodes with similar influence in the SIR model have little  
Figure 6: Comparison between the central value and the propagation ability of SIR. The horizontal axis represents the node influential value obtained by each algorithm and the vertical axis is the propagation capability \(F(t)\) of the corresponding node evaluated by the SIR propagation model. difference from the influence in the TPR algorithm. In Power Grid, the result of the HITS algorithm was better than that of TPR. Then, to evaluate the infection ability of the influential nodes identified by each algorithm, the top 10 influential nodes identified by the DC, BC, PageRank, HITS, and TPR algorithms were selected as the seed nodes of the SIR model. The probability of infection \(\beta\) was 0.3, the recovery probability \(\gamma\) was 1, 20 steps were propagated, and 100 iterations were performed. Finally, the total number of infected and recovery nodes in the network \(F(t)\) were counted to represent the propagation ability of the top 10 nodes selected by each algorithm. The higher the \(F(t)\), the more influential the 10 selected seed nodes. The results are shown in Figure 7.  
From Figure 7, in the Email (Figure 7a) and Protein (Figure 7c) networks, the top 10 nodes identified by each algorithm have similar propagation ability.