# Multivariate Network Layout Using Force-Directed Method with Attribute Constraints
###### Abstract  
Graph visualization with proper layout is widely applied to understand the relationship between entities in a complex system and the topological structure information is mainly used. Real-world graphs often have the community structures property which is ignored in many existing graph layout methods. Thus, we propose a multivariate network layout method using the force-directed method with attribute constraints. This method can effectively take into account the hierarchical structure, connection strength, and quantitative comparison between communities. First, the layout of community centers is generated by a force-directed algorithm in which node count of the community is taken as constraints to enable area balance of community; Second, community force based on node attribute is added in the force-directed algorithm to maintain the community clarity. A visualization system is also developed to allow users to interactively generate community structure-aware layout results. qualitative and quantitative evaluation of the results verifies the usability and effectiveness of the proposed method by comparing it with other methods. visualization; multivariate network; attribute constraint; force-directed +
Footnote †: journal:  
0000-0001-55200-0000-0000-0000-0000-0000-0000-00000-0000-0000-0000-00000-0000-00  
to implement, and extensible, but lacks the use of attribute information. Similarly, the dimensionality reduction method can maintain the structural consistency, but it has poor scalability and also lacks the use of attribute information. The matrix structure [17] displays the connection relationship of the network with an adjacency relationship matrix. The hybrid structure combines the node-link structure with the matrix structure [18]. For multivariate networks, although they clearly display the connection relationship of nodes and the attribute information, the network display lacks visual perception. The attribute structure ignores the structural information of the multivariate network and directly uses the attribute information for layout. It is possible to convert the attributes into coordinates, and then draw the position of the node in the layout space [19]. It is also possible to lay out the network with time attributes according to the time axis [20]. The advantage is that it can display the attribute information of the network without restriction, but the disadvantage is that the visualization lacks structural information, which is not conducive to exploration. To tackle the above problems, in this paper, we propose a multivariate network layout method using the force-directed method with attribute constraints (FDAC). We utilize the network topology and node attribute information, based on the user's choice, to realize the visual exploration of multivariate networks. First, through the interactive selection from users, the attributes of the nodes are obtained and the communities are allocated, to realize the data preprocessing. Then the attribute community layout is performed to obtain the position information of the attribute community of the node. Finally, the node layout is carried out to realize the visualization of multivariate networks. In the layout process, the attribute information of the nodes is fully utilized, and the layout is realized adaptively according to the user selection. We have implemented an interactive visual system to complete the layout task of the entire multivariate network. The source code of FDAC is available at [[https://github.com/tddsa/FDAC](https://github.com/tddsa/FDAC)]([https://github.com/tddsa/FDAC](https://github.com/tddsa/FDAC)) (accessed on 27 April 2022). Overall, our contributions are as follows:  
* We propose a multivariate network layout method FDAC based on attribute constraints. It mainly includes attribute community layout and node layout. Based on the force-directed method, multiple constraints are constructed using attribute information. * We construct an interactive visualization system.