## 5 Results and Discussion
### SIR Spreading Dynamic Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Network** & **DC** & **CC** & **BC** & **EC** & **DC\({}^{+}\)** & **GGC** & **LGI** & **DCGM\({}^{++}\)** & **HSGM** & **NPIC** & **NHM** & **HCGC** \\ \hline Dolphins & 0.8274 & 0.6260 & 0.5590 & 0.6587 & 0.8765 & 0.7963 & 0.7984 & **0.9148** & 0.8566 & 0.8661 & 0.8619 & 0.9074 \\ USAir & 0.7679 & 0.8008 & 0.5758 & 0.8803 & 0.8900 & 0.7471 & 0.8517 & **0.8966** & 0.7886 & 0.8068 & 0.8721 & 0.8922 \\ EEC & 0.8524 & 0.8504 & 0.7254 & 0.9042 & 0.9052 & 0.8404 & 0.8577 & 0.9007 & 0.7648 & 0.8699 & 0.8969 & **0.9058** \\ Email & 0.8000 & 0.8079 & 0.6421 & 0.8634 & 0.8937 & 0.8077 & 0.8517 & 0.8873 & 0.8653 & 0.8326 & 0.8955 & **0.9067** \\ Euroroad & 0.6217 & 0.5933 & 0.4173 & 0.5901 & 0.8217 & 0.7799 & 0.7729 & 0.8193 & 0.6967 & 0.7690 & 0.7944 & **0.8662** \\ Blogs & 0.8603 & 0.7814 & 0.6797 & 0.8584 & 0.8889 & 0.8123 & 0.8454 & 0.8979 & 0.7169 & 0.8759 & 0.8893 & **0.9018** \\ Karate & 0.7890 & 0.7505 & 0.6573 & 0.8441 & 0.8146 & 0.7226 & 0.7178 & **0.9198** & 0.8667 & 0.8477 & 0.9064 & 0.8825 \\ GCliting & 0.7686 & 0.7777 & 0.5505 & 0.8263 & 0.9099 & 0.7727 & 0.8453 & 0.9051 & 0.8636 & 0.8410 & 0.9036 & 0.9241 \\ Celegan & 0.7246 & 0.8182 & 0.5462 & 0.8069 & 0.8664 & 0.8022 & 0.7958 & 0.867 & 0.8687 & 0.8225 & 0.8870 & **0.9118** \\ \hline \end{tabular}
\end{table} 
Table 10: The Kendall’s correlation coefficient of different measures over public real networks. Where \(\beta=\beta_{c}\) and \(R=2\) for a truncation radius. The measure with highest accuracy for each network is highlighted in bold and the measure with the second best is underlined. Figure 2: Comparison of Kendall’s correlation coefficient of different measures on public real networks dataset in range of \(\beta=[0.5\beta_{c},1.5\beta_{c}]\) and \(R=2\). Figure 3 illustrates the spreading capability of different measures through the Kendall's correlation coefficient with a truncation radius \(R=3\) and infection probabilities \(\beta\in[0.5\beta_{c},1.5\beta_{c}]\). Similar to the results of \(R=2\), HCGC outperforms the existing approaches on most of the networks when \(\beta>\beta_{c}\), except for the Karate network. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Network** & **DC** & **CC** & **BC** & **EC** & **DC\({}^{\star}\)** & **GGC** & **LGI** & **DCGM\({}^{\star+}\)** & **HSGM** & **NPIC** & **NHM** & **HCGC** \\ \hline Dolphins & 0.8274 & 0.6260 & 0.5590 & 0.6587 & 0.8765 & 0.7709 & 0.7984 & **0.9148** & 0.8566 & 0.8661 & 0.8619 & 0.9000 \\ USAir & 0.7679 & 0.8008 & 0.5758 & 0.8803 & 0.8900 & 0.7077 & 0.8517 & **0.8964** & 0.7886 & 0.8068 & 0.8866 & 0.8956 \\ EEC & 0.8524 & 0.8504 & 0.7254 & 0.9042 & **0.9052** & 0.8226 & 0.8577 & 0.8985 & 0.7648 & 0.8699 & 0.8969 & 0.9038 \\ Email & 0.8000 & 0.8079 & 0.6421 & 0.8634 & 0.8932 & 0.7770 & 0.8517 & 0.8804 & 0.8653 & 0.8326 & 0.8898 & **0.8989** \\ Euurorad & 0.6217 & 0.5933 & 0.4173 & 0.5901 & 0.8217 & 0.8167 & 0.7729 & 0.8389 & 0.6967 & 0.7690 & 0.8060 & **0.8833** \\ Blogs & 0.8603 & 0.7814 & 0.6797 & 0.8584 & 0.8889 & 0.7911 & 0.8454 & 0.8970 & 0.7169 & 0.8759 & 0.8949 & **0.9012** \\ Karate & 0.7890 & 0.7505 & 0.6573 & 0.8441 & 0.8146 & 0.7034 & 0.7178 & **0.9126** & 0.8667 & 0.8477 & 0.8955 & 0.8982 \\ GDciting & 0.7686 & 0.7777 & 0.5505 & 0.8263 & 0.9099 & 0.7593 & 0.8453 & 0.9089 & 0.8636 & 0.8410 & 0.9095 & **0.9226** \\ Celegan & 0.7246 & 0.8182 & 0.5462 & 0.8069 & 0.8664 & 0.8095 & 0.7958 & 0.8776 & 0.8687 & 0.8225 & 0.9038 & **0.9137** \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The Kendall’s correlation coefficient of different measures over public real networks. Where \(\beta=\beta_{c}\) and \(R=3\) for a truncation radius. The measure with highest accuracy for each network is highlighted in bold and the measure with the second best is underlined. Figure 3: Comparison of Kendall’s correlation coefficient of different measures on the public real networks dataset in range of \(\beta=[0.5\beta_{c},1.5\beta_{c}]\) and \(R=3\).