Research On Self-Similarity Property Of Networks Based On Degree-Degree Distance

With the development of complex network theory and its application,people find that complex network is a good tool to describe the relationship between natural science,social science,management science and engineering technology.As one of the basic topological characteristics of complex network,self-similarity has attracted the attention of many scholars since it was revealed by Song et al through renormalization theory in 2005.This paper focuses on the self-similarity measurement methods of single and multilayer complex networks,and the main work is as follows:1.Research on self-similarity of single-layer networks.At present,fractal dimension calculation method is the main method to calculate the self-similarity of complex network.In the existing fractal dimension calculation method,the distance between nodes is defined as the number of edges contained in the shortest path connecting two nodes.Then,based on the classical box coverage algorithm,a box coverage algorithm model based on degree-degree distance is proposed to analyze whether the single-layer complex network has self-similar characteristics from the perspective of degree-degree distance,and calculate the fractal dimension of the network.The proposed model is used to analyze the constructed small-world networks and four real social networks.Experimental results show that the fractal characteristic of complex networks can be measured from the perspective of degree-degree distance,and verify whether the network has self-similarity.At the same time,the method can also be applied to study the self-similarity of weighted networks.2.Research on self-similarity of multilayer networks.Since most of the existing complex systems are composed of multiple networks interacting with each other,the study of self-similarity of multilayer networks has become an important research topic.Considering the connection relation between each sub-network in the multilayer network,this paper first uses the Shannon entropy theory to evaluate the complexity of each sub-network in the multilayer network,and assigns different weight to each sub-network according to the complexity difference between the sub-networks.Next,the degree-degree distance is used to unify the edge distance between each sub-network layer,and the multilayer network is compressed into a single layer network.Finally,the self-similarity of the aggregation network is studied based on the box covering algorithm.The method is used to calculate a randomly constructed three-layer network,two Sierpinski networks with fractal properties and two real multilayer networks.Among them,the connection mode between two Sierpinski networks is random connection,in order to explore whether the constructed multilayer network still has self-similarity when connecting multiple single layer networks with self-similarity into the multilayer network.Experimental results show that this method can be used to reveal the self-similarity of multilayer networks,and it is found that when multiple sub-networks are connected in different ways,the degree of self-similarity of multilayer networks is different.This experimental result provides a new direction for the study of self-similarity in multilayer networks,which needs further research.