Identification Of Important Motif And Study Of Motif Adjacency Matrix In Directed Weighted Networks

Most real networks are directed weighted networks.The motif structure in the networks can reflect the design principles of the network structure,while the weight represent the frequency of connections between nodes.The directed weighted motifs of the networks not only contain the information of the network microstructure,but also reflect the strength of the structure between nodes,which play an important role in analyzing the structure of the directed weighted networks.In this thesis,weighted motifs are processed in different ways based on the directed weighted networks to identify important types of weighted motif.In addition,the motif adjacency matrix corresponding to weighted motifs are represented by matrix operations.The related research can help to analyze the higher-order structural properties of directed weighted networks.The specific research works are as follows:By defining the edge weight as strong and weak labels,the directed weighted networks are transformed into label networks,and the simple motifs are expanded to label motifs,so as to identify the important motifs in the directed weighted networks.For the label motifs of the three nodes,the time-consuming procedure of subgraph traversal is replaced by the estimated probability of the corresponding number of the motifs appear in the random networks,and the important label motifs in the directed weighted networks are identified by introducing a dynamic indicator associated with the label motif type.It is applied to the passing networks of Guangdong team and Liaoning team in the 2019-2020 finals of China Basketball Association(CBA).The important passing modes of the teams in the games and the important players in the corresponding modes are obtained.The same three-node simple motifs are taken as the research objects.By taking the arithmetic mean value and geometric mean value of the motif edge weight,the motif is weighted as a whole.Based on the connection types of the edges,matrices representing the bidirectional structure,unidirectional structure and borderless structure of the networks are introduced.The matrix expressions of the motif adjacency matrix of directed weighted networks are given by using matrix product and Hadamard product.At the same time,an example is given to test the agreement between the motif adjacency matrix expressions and the weighted idea,and the relationships between the motif adjacency matrix expressions in different network types are analyzed and discussed.The weighted motifs of directed weighted networks contain information about the microstructure of the network and the strength of the structure between nodes.Their related research is beneficial for further understanding the structural characteristics of directed weighted networks.Identifying important label motifs helps to mine important construction patterns and key nodes of directed weighted networks.The matrix operations are used to express the motif adjacency matrix in the networks,which provide convenience for the analysis of the related properties of network higher-order structure using algebraic theory.