# A Method of Node Layout of a Complex Network Based on Community Compression
## 4 Experiments and Analysis
By comparing the layout effects of different methods, it can be seen that the advantages of the method in this paper are mainly reflected in the following two aspects: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Data** & **|V|** & **|E|** & \(\mathbf{C}\) & \(\mathbf{N}_{comm}\) \\ \hline \multirow{4}{*}{Dolphin} & Before & \multirow{2}{*}{62} & \multirow{2}{*}{159} & \multirow{2}{*}{0.303} & \multirow{2}{*}{5} \\  & compression & & & & \\  & Method 1 & & & & \\  & Method 2 & & & & \\  & Method of this & & & & \\  & paper & & & & \\ \hline \multirow{4}{*}{Football} & Before & \multirow{2}{*}{115} & \multirow{2}{*}{613} & \multirow{2}{*}{0.403} & \multirow{2}{*}{10} \\  & compression & & & & \\  & Method 1 & & & & \\  & Method 2 & & & & \\  & Method of this & & & & \\  & paper & & & & \\ \hline \multirow{4}{*}{Karat} & Before & \multirow{2}{*}{34} & \multirow{2}{*}{78} & \multirow{2}{*}{0.588} & \multirow{2}{*}{4} \\  & compression & & & & \\ \cline{1-1}  & Method 1 & & & & \\ \cline{1-1}  & Method 2 & & & & \\ \cline{1-1}  & Method of this & & & & \\ \cline{1-1}  & paper & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of compression results. Figure 4: Layout effect of the football network before and after compression. Figure 3: Layout effect of the dolphin network before and after compression. (1) The compression based on the community structure can retain the community composition of the network and highlight the mesoscale structure characteristics. The sub-graphs (b), (c), and (d) in Figures 3-5 show, respectively, the layout results of the compression network in method 1, method 2, and the method in this paper. Compared with the original network layout results in the sub-graph (a), the number of nodes and the number of edges in the sub-graphs (b), (c), and (d) are compressed to a large extent. The original network in sub-graph (a) is limited by the screen size, with small nodes and dense edges, and the overlap of nodes and edges are serious. In the chaotic overlapping view, it is difficult for users to perceive the overall structure of the network. The three methods mentioned above can reduce the visual clutter caused by overlapping of nodes and edges by reducing the scale of nodes and edges. However, because method 1 (subgraph (b)) and method 2 (subgraph (c)) evaluate the importance of nodes and select network representative nodes based on the global structure, no effective representative nodes are reserved for communities with few nodes or relatively sparse edges. In the process of compression, these communities are compressed and merged, resulting in a decrease in the number of communities, which is unable to accurately display the community composition of the original network. However, the method in this paper (subgraph (d)) is compressed based on the community structure to ensure that each community structure has representative nodes, which avoids the loss of the community in the compression process, and reflects the structural characteristics of the network on the community scale. Figure 5: Layout effect of the karst network before and after multi-granularity compression by the proposed method. In addition, compression based on community structure is more conducive to the perception of the overall structure of the network and the interaction between communities. Taking Figure 3d as an example, it can be found that the original network can be divided into five societies. Among them, \(C_{1}\) and \(C_{5}\) contain a large number of nodes, while the other three have a small number. The interaction between \(C_{1}\) and \(C_{5}\) is mainly realized through \(C_{2}\) and \(C_{3}\). Although there are few nodes in the \(C_{2}\) and \(C_{3}\) communities, they play a \"bridge\" role in the interaction of nodes in the whole network, which is very important to the topology of the network. However, \(C_{2}\) and \(C_{3}\) communities are not retained in Figure 3b,c, which cannot accurately reflect the \"bridge\" role of the \(C_{2}\) and \(C_{3}\) communities.