# A Method of Node Layout of a Complex Network Based on Community Compression
## 4 Experiments and Analysis  
This paper selects three standard data sets in the field of network community analysis: dolphin, football, and karat. Among them, dolphin is the social network of dolphins, football is the social network of the NCAA football league, and karat is the social network of a karate club. The number of nodes and edges of the corresponding network are shown in Table 1.  
The compression layout results of the method of this paper are compared with the network compression layout methods based on node degree value (method 1) and PageRank (method 2). Firstly, the compression effect of different compression methods was quantitatively evaluated through the variations of the number of nodes \(|V|\), the number of edges \(|E|\), the average clustering coefficient \(C\), and the number of communities \(N_{comm}\). The average clustering coefficient indicates the degree of aggregation between nodes in the network, and the calculation formula is  
\[C=\frac{1}{N}{\sum_{i=1}^{N}{\frac{2E_{i}}{k_{i}(k_{i}-1)}}}, \tag{5}\]  
where \(E_{i}\) is the number of the edges that connect to node \(i\), and \(k_{i}\) is the degree of node \(i\). Then, by comparing the visual layout effect of the topological structure before and after compression, the advantages of the method in this paper are qualitatively analyzed. The variation of the number of nodes and the number of edges represents the compression scale of the network. The variation of the average clustering coefficient describes the tightness of connection between nodes in the network. Finally, the variation of the community number reflects whether the compressed network retains the community composition of the original network. In the experiment, the selected node compression ratio was 0.2. That is, in methods 1 and 2, the network representative nodes were selected according to 20% of the total number of nodes in the whole network, and the method in this paper selected the representative nodes of the community structure according to 20% of the total number of nodes in each community. The compression results of the different methods are compared in Table 1. It can be seen that all of the compression methods can reduce the number of nodes and edges to a large extent by merging non-important nodes, thus achieving the purpose of network compression. In addition, the average clustering coefficient of the compressed network is higher than that before compression, which indicates that the three compression methods above all retain closely connected important nodes, and these nodes and their connecting edges can reflect the skeleton structure of the network. Among them, the average clustering coefficients of the compression networks ranked based on node degree value (method 1) and PageRank (method 2) are relatively close, and both of them are larger than the method in this paper. This is because although the first two methods adopt different node importance evaluation models and the node importance ranking results are not same, for the whole network, important nodes are all distributed in the top ranking region. Therefore, compression results based on the importance of nodes in the global network are the same or basically the same set of representative nodes. In this paper, the importance of nodes in different community structures are sorted respectively. The reserved nodes are important nodes in each community structure and represent the internal structure of each community. Although the average clustering coefficient of the compressed network in this paper is relatively low, the number of communities does not decrease. The community composition of the network is relatively intact, and the overall structure of the network is preserved on the medium scale. The first two methods lost part of the community, resulting in an incomplete overall structure of the network. Figures 3-5 show the effect pictures of the three methods used to visually compress the layout of different networks.