Similarity Community Partition Based On Multi-Level Nodes Algorithm Research

Complex network has important research value in graph theory analysis,which involves various disciplines,such as physics,communication,biology and so on.Many scholars have found that although the complex network has the character istics of huge data and intricate connection relationship,it has some important structural characteristics,such as community structure,density and hierarchical connection.In the study of complex networks,some algorithms for community division are proposed to analyze the structural characteristics of communities in complex networks.In this paper,in order to analyze the characteristics of more accurate community division among nodes,by studying the similarity relationship between nodes and combining the advantages of the current community discovery algorithm,a new community division algorithm is proposed and compared with the current popular community division algorithm.Traditional community partition algorithms based on node similarity matrix are mainly based on the similarity matrix constructed by the number of common neighbors between nodes.On this basis,some algorithms also consider the degree matrix between nodes,but the results of community partition are still not very accurate.The community partition algorithm based on node similarity is proposed in this paper.On the basis of common neighbor and degree matrix,the distance matrix between nodes is considered.The improved similarity matrix is not only applicable to the classification of single-layer network communities,but also accurate to the classification of two-layer and multi-layer networks.In this paper,the community division of complex networks is mainly analyzed from two aspects: single level network and multi-level network.In the community division of the single-layer network,through the improved node similarity matrix and the combination of k-means and FCM clustering algorithm,the community division of Zachary network,Dolphins network,American political book network and Football network was carried out.By analyzing the similarity evaluation index of these two algorithms at different levels,the similarity evaluation of the divided communities and the original network communities is carried out.Because the single-layer network considers the neighbor matrix of the node,but for some relatively complex network structures: the number of common neighbors and the shortest distance between two nodes are the same,the neighbor matrix of the neighbor node also needs to be considered.On the basis of constructing the similarity matrix of nodes,the similarity of ambiguous nodes is considered.Based on this,a method for computing node similarity in multilayer networks is further defined.Based on the community analysis of the two-layer network,this paper only defines the similarity calculation formula for the multi-layer complex network,and the community division steps are similar to the two-layer network.The similarity matrix of the network is calculated by the multi-level node similarity calculation formula.In the community division of the two-layer network,on the basis of similarity matrix,k-means and FCM algorithm are used to classify the four kinds of complex networks,and then similarity analysis is conducted between the divid ed communities and the original network communities through similarity evaluation index.Through the analysis and comparison of the results,it can be concluded that the community algorithm similarity value of multi-level network is generally higher than that of single-level network.K-means algorithm is suitable for complex networks with large amount of data,while FCM algorithm is suitable for network models with small amount of data.Moreover,the similarity evaluation index value of k-means algorithm is higher than that of FCM algorithm,and the community division effect is more accurate.