Table 1.
Performances of reconstruction and locating hidden source.
| Network reconstruction | Error of λ | LHS | |||||||
|---|---|---|---|---|---|---|---|---|---|
| SREL | SRNC | TPR | FPR | Mean | Min | Max | TPR | FPR | |
| SIS | |||||||||
| WS | 1.0 | 1.0 | 1.0 | 0.0 | 0.008 | 0.0 | 0.042 | 1.0 | 0.001 |
| ER | 0.992 | 0.991 | 0.992 | 0.009 | 0.014 | 0.0 | 0.192 | 0.977 | 0.026 |
| BA | 0.977 | 0.986 | 0.977 | 0.014 | 0.046 | 0.0 | 1.881 | 0.99 | 0.066 |
| prison | 0.994 | 0.993 | 0.994 | 0.007 | 0.032 | 0.0 | 0.311 | 1.0 | 0.017 |
| Santafe | 0.978 | 0.991 | 0.978 | 0.009 | 0.063 | 0.0 | 1.122 | 1.0 | 0.041 |
| netscience | 0.959 | 0.992 | 0.959 | 0.008 | 0.172 | 0.0 | 2.878 | 0.949 | 0.144 |
| NW | 1.0 | 0.999 | 1.0 | 0.001 | 0.015 | 0.0 | 0.15 | 1.0 | 0.001 |
| ZK | 0.981 | 0.993 | 0.981 | 0.007 | 0.079 | 0.001 | 0.712 | 0.97 | 0.078 |
| Polbooks | 0.932 | 0.984 | 0.932 | 0.016 | 0.133 | 0.0 | 1.1875 | 0.732 | 0.234 |
| Football | 0.970 | 0.989 | 0.970 | 0.011 | 0.166 | 0.001 | 0.651 | 0.612 | 0.021 |
| Dolphin | 0.952 | 0.967 | 0.952 | 0.033 | 0.022 | 0.001 | 0.123 | 0.925 | 0.083 |
| Leadership | 0.975 | 0.986 | 0.975 | 0.014 | 0.05 | 0.0 | 0.706 | 0.869 | 0.057 |
| CP | |||||||||
| WS | 1.0 | 1.0 | 1.0 | 0.0 | 0.009 | 0.0 | 0.048 | 0.936 | 0.068 |
| ER | 0.999 | 1.0 | 1.0 | 0.0 | 0.01 | 0.0 | 0.073 | 0.925 | 0.327 |
| BA | 0.997 | 1.0 | 1.0 | 0.0 | 0.008 | 0.0 | 0.043 | 0.943 | 0.08 |
| Prison | 0.995 | 0.996 | 0.996 | 0.004 | 0.005 | 0.0 | 0.018 | 0.911 | 0.012 |
| Santafe | 0.984 | 0.996 | 0.996 | 0.004 | 0.006 | 0.0 | 0.036 | 0.929 | 0.034 |
| Netscience | 0.996 | 0.999 | 0.996 | 0.001 | 0.007 | 0.0 | 0.166 | 1.0 | 0.050 |
| NW | 1.0 | 1.0 | 1.0 | 0.0 | 0.009 | 0.0 | 0.052 | 0.98 | 0.034 |
| ZK | 0.992 | 0.992 | 0.992 | 0.008 | 0.007 | 0.001 | 0.022 | 0.977 | 0.028 |
| Polbooks | 0.973 | 0.995 | 0.973 | 0.005 | 0.008 | 0.0 | 0.042 | 0.829 | 0.386 |
| Football | 0.995 | 0.997 | 0.995 | 0.003 | 0.006 | 0.0 | 0.028 | 0.517 | 0.015 |
| Dolphin | 0.952 | 0.971 | 0.971 | 0.029 | 0.006 | 0.0 | 0.026 | 0.786 | 0.059 |
| Leadership | 0.996 | 0.993 | 0.993 | 0.007 | 0.006 | 0.0 | 0.013 | 0.857 | 0.075 |
FPR, false positive rate; LHS, locating hidden source; SREL, success rates for existent link; SRNC, success rates for null connection; TPR, true positive rate.
The accuracy of network reconstruction is quantified by the success rates SREL and SRNC, as well as the trade-off measures TPR and FPR. The accuracy in determining the values of the infection rate λ is characterized by the relative mean errors, the minimum and maximum errors. The accuracy of LHS is characterized by the trade-off measures TPR and FPR. The results of network reconstruction and error in λ are obtained from 30 independent realizations. The results of LHS is obtained from ten dynamical realizations and ten configurations of the hidden source. Other parameters are the same as in Fig. 2. For data sources, reference and network models, see Supplementary Table 1 and Supplementary Note 10.