Research On Coarse Graining And Synchronization Performance Of Complex Multilayer Directed Network Based On Connection Graph

From the perspective of graph theory,the complex characteristics of complex networks are manifested in numerous nodes,complex topology structures,and complex coupling relationships.The study of complex networks can help people to describe various networks that are common in life,such as the national power grid,the city's transportation network and so on.Complex network is an interdisciplinary subject with wide application and strong intersection with other disciplines.With the increasing development of network science,a wave of research on complex networks has sprung up.Synchronization phenomenon is common in people's life,such as the synchronous flicker and extinction of fireflies in the forest and so on.Synchronization of complex networks also plays a very important role in communication systems,medicine,biology and other fields.The scale of complex networks is generally very large,which is not conducive to people's research on problems such as synchronization performance.Therefore,when reducing the network size,people propose a coarse-grained method of the network,that is,while reducing the network size,the original network characteristics such as coupling relationship are retained..In recent years,the research of single-layer undirected complex networks has achieved fruitful research results.However,in people's real life,the networks are related.Various associated networks exist in the form of double-layer or even multi-layer,and the network is not undirected.Undirected networks can not respond to the real connection relationship between nodes,and there are one-way or two-way connections in the network.To address these issues,this paper studies the following:1.First of all,for the convenience of research,a generalized nearest neighbor network model is established.Based on this model,by setting weights,it is divided into a weighted directed network and an unweighted directed network,and these two models are extended into a multi-layer directed network.network,and the coupling strength between layers is different from the coupling strength within layers.2.The idea of coarse-granularity is applied to reduce the network scale.When the connection strength between nodes is the same,the nodes with the same out-degree and in-degree as their neighbors are merged.When the connection strength between nodes is different(there is weight in the connection edge),the similarity of nodes is utilized and the algorithm is used to find similar nodes for merging,and the original coupling information of nodes is retained.3.When studying the network synchronization problem,the connection graph method is used for calculation and derivation,which avoids the use of the principal stable function method to obtain eigenvalues.Facing the multi-layer network,in order to simplify the calculation,the given network combination characteristics are fully utilized,and the network is divided into two parts.Layer calculation,it is concluded that the simplified network has enhanced synchronization ability compared with the network before simplification.4.In order to verify the correctness of the derivation results,three-layer and five-layer directed coupled networks and their corresponding simplified network models are established,and the accuracy of the derivation results is verified by simulating the synchronization process on the model.