# A Method of Node Layout of a Complex Network Based on Community Compression
## 2 Related Work  
In the field of network visualization compression layout, the spring model [9] has been most widely explored because of the advantages of simplicity, efficiency, and easy understanding. It simulates the whole network as a spring system, and finally achieves the force balance of the nodes by calculating the force controlled by the distance between different nodes. The KK (Kamada-Kawai) algorithm [10] introduces [PERSON]'s law on the basis of the spring model, calculates system energy according to the stress state of the nodes, and transforms the optimal layout problem of nodes into the solution problem of minimizing system energy, which makes the convergence speed of the layout process obviously increase. In the DH (Davidson-Harel) algorithm [11], the constraints of many aesthetic standards are taken into consideration to construct the energy function, such as node location, length of joints, and the intersection of edges. Different layout effects can be achieved by the parameters of the energy function model. In the FR (Fruchterman-Reingold) algorithm [12], the nodes are modeled as charged particles in the physical system, and the charge repulsion forces are introduced between particles. The smaller the distance between the particles, the greater the repulsion force is, which can reduce the overlap phenomenon of the dense nodes to a certain extent. The simulated annealing algorithm was adopted by introducing a \"cooling function\" in order to make the algorithm converge quickly, which can gradually reduce the moving step of the nodes and makes the system energy decrease rapidly, thus realizing the goal of rapid layout [13; 14]. Compared with the KK and DH algorithms, the rendering results from the FR algorithm have better symmetry and clustering layout effects in most network visualization applications, and are more in line with aesthetic standards. Many scholars have further studied the basis of the FR model. On the one hand, it proposes a fast multi-scale layout [15], multi-level layout [16], and FADE [17] algorithm to reduce visual confusion and accelerate layout. On the other hand, it proposes a network visualization method based on community structure [18] or subgroup analysis [19]. The above method shows the community composition of the network to a certain extent, but it is far from sufficient to analyze the mesoscale features. Studies on network compression are mainly based on the importance of nodes or edges. [PERSON] et al. [20] studied the nearest neighbor search problem in complex networks by proposing an appropriate concept of proximity degree. Applying it to the problem of network community detection, it can explore the community structure of real networks better. This gave us the idea of studying the reasonable compression layout scheme of community structure. [PERSON] et al. [21] proposed a sparse representation of network structure based on geometric multi-scale analysis, which effectively helps to analyze the network with as little information as possible. [PERSON] et al. [22] divided network nodes based on the K-core concept in complex networks, and used the force-directed layout algorithm to realize the visualization of a compressed large-scale complex network. However, the above methods evaluate the importance of nodes based on the global network, choose the important nodes as the representative nodes of the overall network structure, and compress the non-important nodes at the same time, so as to achieve the goal of network compression. This kind of method retains the core structure of the network from the node scale (microscale), but it ignores the community structure of the network and cannot show the structural characteristics of the network from the mesoscale. Based on data fields, the authors of [23] described the potential values of nodes in the network affected by the nodes themselves and their neighboring nodes by calculating their topological potentials, which can more truly describe the importance of nodes in the network structure.