The Multi-granularity in Graph Revealed by a Generalized Leading Tree

Abstract: There are hierarchical characteristics in the network and how to effectively reveal the hierarchical characteristics in the network is a problem in the research of network structure. If a node is assigned to the community to which it belongs, how to assign the community to a higher level of community to which it belongs is a problem. In this paper, the density of data points is investigated based on the clustering task. By forming the density of data points, the hierarchical difference of data points is constructed. In combination with the distance between data points, a density-based leading tree can be constructed. But in a graph structure, it is a problem to build a lead tree that reveals the hierarchical relationships of the nodes on the graph. Based on the method of tree formation based on density, this paper extends the model of leading tree to the hierarchical structure of graph nodes, discusses the importance of graph nodes, and forms a leading tree that can reveal the hierarchical structure of graph nodes and the dependency of community. Experiments were carried out on real data sets, and a tree structure was formed in the experiment. This graph leading tree can well reveal the hierarchical relationships in the graph structure.