# Locating the Epidemic Source in Complex Networks with Sparse Observers
## 3 Experiments and Analysis
### Source Localization Accuracy in Empirical Networks
It can be seen from the results that the performance of PESL algorithm in all empirical networks except URV network is consistently better than that of other algorithms. When there is a lower infection probability, the spread process has stronger randomness. Although at this time GAU and TRBS algorithms consider location information and time information of observers, their behavior is not better than DC and JC algorithms only considering the location information especially in Hospital and ACM networks. When the infection probability increases, GAU and TRBS will gradually show their wonderful performance. Figure 8 shows the relationship between the performance of source localization algorithm and the reporting probability. Similar to the previous situation, PESL algorithm still has a great source localization performance. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Type** & **Name** & \(N\) & \(M\) & \(\langle k\rangle\) & \(k_{max}\) & \(H\) & \(\langle d\rangle\) & \(\langle C\rangle\) \\ \hline Contact & Hospital & 75 & 1139 & 30.373 & 61 & 1.244 & 1.598 & 0.640 \\ Contact & Workplace & 92 & 755 & 16.413 & 44 & 1.213 & 1.964 & 0.426 \\ Contact & ACM & 113 & 2196 & 38.867 & 98 & 1.223 & 1.656 & 0.535 \\ Contact & School & 327 & 5818 & 35.584 & 87 & 1.144 & 2.159 & 0.504 \\ Contact & Infectious & 410 & 2765 & 13.488 & 50 & 1.388 & 3.631 & 0.456 \\ Communication & URV & 1133 & 5451 & 9.622 & 71 & 1.942 & 3.606 & 0.220 \\ Biological & Yeast & 1458 & 1948 & 2.672 & 56 & 2.667 & 6.812 & 0.071 \\ Transport & OpenFlights & 3397 & 19,230 & 11.322 & 248 & 5.699 & 4.103 & 0.488 \\ Contact & Sex & 15,810 & 38,540 & 4.875 & 305 & 5.828 & 5.785 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Basic topological properties of nine various networks. Where \(N,M\) represent the number of nodes and edges, \(\langle k\rangle\) and \(k_{max}\) denote the average degree and maximum degree, \(H\) means index of degree heterogeneity, \(\langle d\rangle\) is the mean shortest path length and \(\langle C\rangle\) represents mean local clustering coefficient. Figure 8: The performance of epidemic source localization accuracy in empirical networks under various reporting probabilities with five algorithms. (**a-i**) represent the results in Hospital, Workplace, ACM, School, Infectious, URV, Yeast, OpenFlights and Sex network respectively. In the figure, the abscissa represents the reporting probability of nodes \(\delta\), the ordinate denotes the distance between the real source and the source found by different source localization algorithms. The number of observers is similar to Figure 7. The infection probability used in the simulation was \(\beta=0.2\) and the recovery probability was \(\gamma=0.1\). Figure 7: The performance of epidemic source localization accuracy under various infection probability with five algorithms in empirical networks. The number of observers changes due to the scale of network. In (**a-e**), \(K=10\); in (**f-h**), \(K=25\); in (**i**), \(K=50\). The recovery probability used in the simulation is \(\gamma=0.1\) and the reporting probability of nodes is \(\delta=0.3\).