# A Method of Node Layout of a Complex Network Based on Community Compression
## 1 Introduction  
The purpose of network visualization is to assist users to perceive the network structure and understand and explore patterns hidden in the network data [1; 2]. However, the details of all the nodes and edges, which are shown in their entirety on a limited-size screen, is not a good solution, and it may cause the following problems from a visualization point of view. On the one hand, when a complex network with large numbers of nodes and high-density edges is visualized on a limited-size screen, users fall easily into a chaotic and overlapping node-connection diagram, where it is difficult to identify and perceive the overall structure of the network, and the users cannot easily find elements of interest. On the other hand, the large amount of data inevitably brings greater computational pressure and higher requirements on the algorithms and hardware. In short, inefficient or time-consuming network visualization loses its meaning. Until now, the existing work of complex networks has been limited to the local scale structure, obtained through statistical distribution, or the macroscopic scale of the overall parameters of the network. However, these two levels can be understood through the intermediate level, which iscalled the mesoscale structure [3]. A mesoscale can be understood as a substructure or subgraph. Substructures have their own topological entities, such as motifs, cliques, cores, and loops, but usually they describe the community [4]. The research of network synchronization processes actually involves studying the evolution process of the dynamic behavior of the network from a small to a large scale, which is inseparable from the mesoscale characteristics of complex networks [5]. In order to display information effectively and assist users in perceiving the mesoscale structure of the network, a large-scale network must be reduced to bring down the user's perception complexity and the computational complexity of the layout process. According to the purpose of reduction, the methods of network reduction processing can be divided into three types: filtering, sampling, and compression. Filtering means to filter the nodes and edges that satisfy the condition by a single attribute or a combination of multiple attributes in the network, thereby reducing the number of nodes and the density of the edges. Filtering technology is more about further refinement and exploration of network data, which needs a certain understanding of the network structure. For example, the elements that meet the requirements are selected and displayed on the screen, according to the degree, the intermediate centrality, the intermediate centrality of nodes, the weight of edges, or any other attributes. Sampling is to select the representative nodes and edges according to a certain sampling strategy and to reflect the structural characteristics of the original network with as few nodes and edges as possible. Common sampling strategies [6] include random node selection, random edge selection, random walk, and sampling strategies based on topological layered models. Compared with filtering and sampling, compression is achieved by aggregating nodes or edges with certain similarities and adopting new nodes instead of aggregation [7]. While reducing the scale of the nodes, it can also ensure the integrity of the network and display the subgraphs of the network. The composition and other characteristics help users perceive the overall structure of the network from the mesoscale structure [8]. For the purpose of effectively displaying mesoscale structure characteristics of the network, a method of node layout of a complex network based on community compression is proposed, which combines the force-directed layout algorithm with the method of network compression based on node importance in community structure.