Eigenvalues of transition weight matrix for a family of weighted networks

Author:

Su Jing12,Wang Xiaomin12,Zhang Mingjun345,Yao Bing6

Affiliation:

1. School of Electronics Engineering and Computer Science, Peking University , Beijing 100871 , China

2. Key Laboratory of High Confidence Software Technologies, Peking University , Beijing 100871 , China

3. China Northwest Center of Financial Research, Lanzhou University of Finance and Economics , Lanzhou 730020 , China

4. School of Information Engineering, Lanzhou University of Finance and Economics , Lanzhou 730020 , China

5. Key Laboratory of E-Business Technology and Application , Lanzhou 730020 , China

6. College of Mathematics and Statistics, Northwest Normal University , Lanzhou, 730070 , China

Abstract

Abstract In this article, we design a family of scale-free networks and study its random target access time and weighted spanning trees through the eigenvalues of transition weight matrix. First, we build a type of fractal network with a weight factor r r and a parameter m m . Then, we obtain all the eigenvalues of its transition weight matrix by revealing the recursive relationship between eigenvalues in every two consecutive time steps and obtain the multiplicities corresponding to these eigenvalues. Furthermore, we provide a closed-form expression of the random target access time for the network studied. The obtained results show that the random target access is not affected by the weight; it is only affected by parameters m m and t t . Finally, we also enumerate the weighted spanning trees of the studied networks through the obtained eigenvalues.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3