# Overlapping Community Detection of Bipartite Networks Based on a Novel Community Density
## 5 Experimental Evaluation
### Experiments on Real-World Bipartite Network  
In this section, we will verify the performance of the DSNE algorithm in the real world network, the CBG&BEN algorithm, and LOCD algorithm is used as the comparison algorithm, and eleven real bipartite network datasets from different domains are used as the dataset to evaluate the DSNE algorithm. The detailed information of these networks is shown in Table 4, where \(m\) and \(n\) represent the number of different types of nodes in the bipartite network, \(|E|\) represents the number of edges between nodes, and \(<k>\) represents the average degree of the network. Taking the SAC dataset in Figure 2 as an example, there are six U nodes and five V nodes, and the network has a total of thirteen edges, so \(m=6\), \(n=5\), \(|E|=13\), and \(<k>~{}=\frac{13+13}{5+6}=2.36\). In order to explain the better understand the dataset we used in Table 4, the South African Companies Bipartite Network (SAC) is taken as an example to illustrate. Figure 2 shows the SAC dataset. Among them, the square nodes (U1 to U6) represent different leaders, the round nodes (V1 to V5) represent different companies, and the edges between nodes represent the leadership relationship between leaders and companies. The community detection results after DSNE algorithm is run are given in Figure 1. The merged community set NC contains two communities, which are, respectively, \(NG_{1}(U_{1},V_{1},E_{1})\) \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name** & \(|E|\) & \(<k>\) & \(m\) & \(n\) & **Description** \\ \hline SAC & 13 & 2.36 & 6 & 5 & South African Companies [6] \\ SW & 89 & 5.56 & 14 & 18 & Southern Women network [40] \\ CLUB & 95 & 4.75 & 25 & 15 & Club membership network [41] \\ CL & 99 & 4.5 & 20 & 24 & Corporate Leadership network [42] \\ AR & 169 & 2.27 & 136 & 5 & American revolution network [43] \\ DUS & 225 & 7.73 & 50 & 9 & Divorce in the United States [44] \\ GP & 1225 & 3.79 & 314 & 360 & Graph Product network [45] \\ CRIME & 1476 & 2.14 & 829 & 551 & Crime network [46] \\ MARIA & 2965 & 5.38 & 297 & 806 & Malaria gene substring network [47] \\ PCD & 3690 & 1.75 & 680 & 739 & Protein complex-drug network [48] \\ COL & 58,595 & 3.02 & 16,727 & 22,015 & Collaboration network [49] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Details of 11 real-world networks. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\lambda\) & \(N\) = 64 & \(N\) = 128 & \(N\) = 256 \\ \hline
0.5 & 34\% & 23\% & 57\% \\
0.6 & 25\% & 38\% & 24\% \\
0.7 & 31\% & 27\% & 3\% \\
0.8 & 18\% & 15\% & 2\% \\
0.9 & 40\% & 10\% & 2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: NMI decreasing speed with noise increasing (\(\lambda\) decreasing) under different \(N\). and \(NG_{2}(U_{2},V_{1},E_{2})\). In \(NG_{1}(U_{1},V_{1},E_{1})\), \(U_{1}=\{U1,U2,U3,U4\}\), \(V_{1}=\{V1,V2,V3,V4\}\), \(E_{1}=\{(e_{(U1,V1)},e_{(U1,V2)},e_{(U1,V3)},e_{(U2,V1)},e_{(U2,V3)},e_{(U3,V3)},e_{( U3,V4)},e_{(U4,V1)},e_{(U4,V3)})\}\). In \(NG_{2}(U_{2},V_{1},E_{2})\), \(U_{2}=\{U5,U6\}\), \(V_{2}=\{V1,V2,V5\}\), \(E_{2}=\{e_{(U5,V2)},e_{(U5,V5)},e_{(U6,V1)},\)\(e_{(U6,V2)}\}\). Table 5 shows the number of communities found in the 11 datasets by the three methods. Table 5 shows that the DSNE algorithm and CBG&BEN algorithm can effectively get the number of communities, while the LOCD algorithm cannot effectively get the community structure in some datasets. LOCD algorithm cannot effectively obtain the number of SAC communities; the main reason is that the SAC dataset contains too little network information than the LOCD algorithm, so the number of communities obtained in the SAC dataset using the LOCD algorithm is 1. In the COL dataset, the LOCD algorithm is considered ineffective because it still fails to obtain sufficient community numbers after a long time (6 h) of operation. In most datasets, the number of communities is not always the more, the better.