# A Method of Node Layout of a Complex Network Based on Community Compression
## 4 Experiments and Analysis
\(C_{4}\) directly interacts with \(C_{1}\), which easily causes deviation in users' understanding of the structural features of the network at the mesoscopic scale. (2) Use of the multi-granularity community structure division algorithm can display the basic structure of the community and realize the multi-granularity compression layout of the network. In this paper, the fringe nodes are compressed while the necessary community structure representative nodes are preserved. Based on the analysis of the importance of nodes based on topological potential, the reserved nodes make a greater contribution to the community composition, reflecting the basic structure of the community. By retaining these nodes and connections, the basic structure of the community can be clearly displayed. At the same time, by compressing non-important nodes and deleting repeated edges, the number of edges within the community is reduced, which is conducive to the visual perception of the community structure and the discovery of important nodes in the community or network structure. According to the granularity of community structure division and compression, the original network can be divided into multi-granularity communities. Table 2 shows the results of multi-granularity compression, where the reserved nodes are underlined. Based on the method proposed in this paper, the number of nodes and the number of edges can be reduced by compressing and merging fringe nodes, so as to realize the multi-granularity compression layout. Subgraphs (d), (e), and (f) in Figure 5 show the three-level compression layout for the karat network data. In stage 1, nodes in the karat network are divided into eight communities based on the Louvain algorithm, while they are divided into four communities in stage 2. Accordingly, the karat network is compressed into eight communities in sub-graph (d) and four communities in sub-graph (e), by compressing each community. In stage 3, nodes in the karat network are also divided into eight communities. However, the network compression ratio can be controlled according to the node compression ratio, and a community can be compressed into one node at most, as shown in stage 3 of Table 2 and Figure 5f. In Figure 5f, each node represents a community, and \"nodes\" 1, 32, and 34 can interact directly with each other, while \"node\" 6 can only interact with other \"nodes\" through \"node\" 1. It is possible to observe the mesoscale structural features at different granularities of the network topology from subgraphs (d), (e), and (f) in Figure 5. \begin{table}
\begin{tabular}{c c} \hline \hline
**Stage** & **Communities** \\ \hline \multirow{4}{*}{1} & \(C_{1}=\{1,\,3,\,4,\,8,\,12,\,13,\,14,\,18,\,20,\,22\}\), \(C_{2}=\{2,\,18,\,20\}\), \\  & \(C_{3}=\{5,\,7,\,11\}\), \(C_{4}=\{6,\,17\}\), \\  & \(C_{5}=\{30,\,26\}\), \(C_{6}=\{32,\,25,\,29\}\), \\  & \(C_{7}=\{28,\,9,\,27,\,30,\,31\}\), \(C_{8}=\{33,\,34,\,10,\,15,\,16,\,19,\,21,\,23,\,24\}\) \\ \hline \multirow{4}{*}{2} & \(C_{1}=\{1,\,2,\,3,\,4,\,8,\,12,\,13,\,14,\,18,\,20,\,22\}\), \(C_{2}=\{6,\,5,\,7,\,11,\,17\}\), \\  & \(C_{3}=\{32,\,25,\,26,\,29\}\), \(C_{4}=\{9,\,33,\,34,\,10,\,15,\,16,\,19,\,21,\,23,\,24,\,27,\,28,\,30,\,31\}\) \\ \hline \multirow{4}{*}{3} & \(C_{1}=\{1,\,2,\,3,\,4,\,8,\,12,\,13,\,14,\,18,\,20,\,22\}\), \(C_{2}=\{6,\,5,\,7,\,11,\,17\}\), \\  & \(C_{3}=\{32,\,25,\,26,\,29\}\), \(C_{4}=\{34,\,9,\,33,\,10,\,15,\,16,\,19,\,21,\,23,\,24,\,27,\,28,\,30,\,31\}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of multi-granularity compression of the karat network.