## 5 Results and Discussion
### Imprecision Function Results  
Table 12 demonstrates the imprecision function values of baseline measures and our proposed algorithm on the public real networks dataset. HCGC with \(R=2\) achieves the highest values compared to others on four networks including Email, Euroroad, Blogs, and Celegan. The proposed measure slightly underperforms the EC on the EEC network.  
Table 13 represents the imprecision function values of baseline measures and our proposed algorithm on public real networks dataset. HCGC with \(R=3\) achieves the highest values compared to others on four networks including Email, Euroroad, Blogs and Celegan. Comparing between the proposed method with \(R=2\) and \(R=3\), HCGC with \(R=3\) shows better evaluation on USAir, Euroroad, Karate, and GDciting networks.  
Figures 4 and 5 illustrate the imprecision function values across different measures. The horizontal axis refers to the fractions of top nodes in the network (p) ranging from 0.01 to 0.2. The vertical axis shows the calculated values of the imprecision function based on the specific algorithm \(\epsilon(p)\). Based on the curves, they show that our method presents significantly high performance (lower is better) compared to the traditional methods on the Euroroad network. Moreover, HCGC has curves that are similar to DCGM\({}^{++}\) and NHM on USAir, Email, Blogs, Karate, and GDciting networks.  
\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\({}^{+}\)** & **GGC** & **LGI** & **DCGM\({}^{++}\)** & **H5 GM** & **NPIC** & **NHM** & **HCGC** \\ \hline Dolphins & 0.1031 & 0.2322 & 0.3082 & 0.0932 & 0.1022 & 0.1381 & 0.1829 & 0.0863 & 0.0908 & **0.0810** & 0.0977 \\ USAir & 0.1250 & **0.1226** & 0.2358 & 0.1351 & 0.1293 & 0.1387 & 0.1389 & 0.1247 & 0.1286 & 0.1262 & 0.1282 & 0.1340 \\ EEC & 0.1944 & 0.1829 & 0.2567 & **0.1681** & 0.1714 & 0.1932 & 0.1760 & 0.1764 & 0.2132 & 0.1815 & 0.1770 & 0.1683 \\ Email & 0.2254 & 0.2154 & 0.2734 & 0.2208 & **0.2037** & 0.2177 & 0.2240 & 0.2072 & 0.2094 & 0.2151 & 0.2061 & 0.2058 \\ Euroroad & 0.1787 & 0.3034 & 0.3750 & 0.2104 & 0.1208 & 0.1444 & 0.2176 & 0.1238 & 0.1685 & 0.1430 & 0.1399 & **0.1091** \\ Blogs & 0.2093 & 0.2606 & 0.2987 & 0.2044 & 0.1836 & 0.2249 & 0.2002 & 0.1939 & 0.2132 & 0.1970 & 0.1917 & **0.1831** \\ Karate & 0.0812 & 0.1317 & 0.0708 & 0.0883 & 0.0783 & 0.0876 & 0.3177 & 0.0646 & 0.0812 & **0.0635** & 0.0788 & 0.0766 \\ GDciting & 0.1911 & 0.1897 & 0.3679 & 0.1512 & 0.1458 & 0.1903 & **0.1455** & 0.1588 & 0.1656 & 0.1626 & 0.1492 & 0.1474 \\ Celegan & 0.2128 & 0.1915 & 0.3551 & 0.1058 & 0.1095 & 0.1660 & 0.1433 & 0.1242 & 0.1487 & 0.1374 & 0.1151 & **0.1014** \\ \hline \hline \end{tabular}
\end{table}
Table 13: Imprecision function of different measures over public real networks, where \(R=3\) 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.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Network** & **DC** & **CC** & **BC** & **EC** & **DC\({}^{+}\)** & **GGC** & **LGI** & **DCGM\({}^{++}\)** & **H5 GM** & **NPIC** & **NHM** & **HCGC** \\ \hline Dolphins & 0.1031 & 0.2322 & 0.3082 & 0.0932 & 0.1022 & 0.1326 & 0.1829 & 0.0909 & 0.0863 & 0.0908 & **0.0810** & 0.1007 \\ USAir & 0.1250 & **0.1226** & 0.2358 & 0.1351 & 0.1293 & 0.1385 & 0.1389 & 0.1247 & 0.1286 & 0.1262 & 0.1275 & 0.1340 \\ EEC & 0.1944 & 0.1829  
Table 14 presents the average imprecision function values across all networks for different measures. The results show that our proposed method outperforms other methods with the lowest imprecision function values for both truncation radii \(R=2\) and \(R=3\). DC\({}^{+}\) is the second-best performing measure.