Related Properties Of Two Special Weighted Networks

In this paper,we introduce two special weighted networks: single-weighted and doublelayer networks,double-weighted and single-layer networks.On this basis,we study properties of average receiving time and average weighted shortest path which reflect the transmission efficiency.The paper is divided into three parts: the scaling of average receiving time and average weighted shortest path on weighted crystal networks,variance of the first return time and decomposition of the first receiving time on weighted double-layer Koch networks as well as the scaling of average receiving time on double-weighted polygon networks.The first two models belong to single-weighted and double-layer networks,the third model is double-weighted and single-layer networks.Chapter 1 mainly describes the research background,development and topological properties of complex networks,introduces weighted networks and random walk,and clarizes the research context and innovation points of this paper.Chapter 2 introduces some basic knowledge and concepts that need to be used in the research of network models.Chapter 3 and chapter 4 introduce two single-weighted and double-layer networks: weighted crystal networks and weighted double-layer Koch networks.In chapter 3,general formulas of average receiving time and average weighted shortest path are derived by block method according to particularity of the networks structure,which are suitable for a class of crystal networks with even edges.Taking hexagonal crystal networks as an example,the calculation process and scaling results are given.Besides,the factors affecting average receiving time and average weighted shortest path are analyzed by means of numerical simulation.At the end of chapter3,the special weighted crystal networks is extended to general crystal networks.For weighted double-layer Koch networks,chapter 4 deduces recursive relation about the first return time and the first receiving time,as well as variance of the first return time by means of probability generation function.Meanwhile,a method is proposed to decompose the first receiving time by converting probability into power based on power networks knowledge.In chapter 5,we study a class of double-weighted and single-layer networks: doubleweighted polygon networks,which is different from conventional iterative networks.Two weighted factors representing different meanings are assigned to each edge of the networks.Exact expression of average receiving time on any double-weighted polygon networks is given by dividing the networks structure and the model of double-weighted Koch networks is extended from triangle to arbitrary polygon.In addition,the power law relationship between average receiving time and networks size is analyzed by taking double-weighted quadrilateral networks as an example.