Research On The Measure Of Network Structure Uniformity Based On Entropy

As a highly abstraction of real system,complex network provides a vital means for the study on systems.The vast majority of systems in reality are heterogeneous,which impacts the transfer of online information,spreading of viruses and survivability.Uniformity of network is a typical feature of network heterogeneity.This paper explores the measurement of network's uniformity based on entropy to find out ways of defining network's structural entropy.The reality of the network structure is diverse,which determines that there is no network structure entropy can describe and compare all non-uniformity of networks.Different forms of network structure entropy are needed to reflect network uniformity from different aspects.In addition,networks in reality are evolving.It is an important problem to guide and control the change of network structure on the basis of existing network structure and make the network uniformity be optimized in the process of evolution.In this paper,the entropy-based network structure uniformity measurement and the uniformity optimization method are studied.The main research work and innovation are as follows:(1).Two new uniformity measurements of unweighted network structure are proposed.On the one hand,some entropy indexes are applied to the uniformity of network structure,including degree distribution entropy,relative value entropy and point-edge difference entropy.On the other hand,benchmark difference entropy and the relative betweenness entropy are designed to measure the uniformity of the network structure.At the same time,this paper analyzes and compares the five unweighted network structure entropy through simulation experiment in different network size,network type,network density to understand the connotation and application of different indicators.(2).The uniformity measurement of weighted network structure is proposed.According to the characteristics of weighted network structure,considering the topology and edge weight,the entropy of the network structure is extended to the weighted network model.Three new weighted network structure entropy are proposed,which are based on relative intensity,point and edge difference and relative betweenness.At the same time,through the design of the simulation experiment,the uniformity of the weighted network with the small-scale evolution is analyzed based on these three measures.(3).An optimization model of network structure uniformity based on entropy is proposed.Aiming at the problem of adding the given number of edges on the basis of the original network structure and how to optimize the network uniformity,the uniformity optimization model is established based on the network structure entropy.At the same time,the network homogeneity optimization algorithm based on taboo search is designed,and the feasibility of the method of network uniformity optimization based on entropy is verified by simulation experiments.(4)The application of entropy-based network structure uniformity is presented by applying examples.Based on the data of 7 semesters of message network,we constructed unweighted message network and weighted message network model.Based on the analysis of the uniformity of 7 semesters message network and optimization of edges addition on the 7th semester message network,this paper presents the network uniformity measurement and optimization of weighted and unweighted network.