搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

网络规模衰减的随机生灭网络平均度

张晓军 钟守铭

引用本文:
Citation:

网络规模衰减的随机生灭网络平均度

张晓军, 钟守铭

Average degree under different network sizes for random birth-and-death networks

Zhang Xiao-Jun, Zhong Shou-Ming
PDF
导出引用
  • 在社会和生物网络中,每个智能体都存在生与灭过程,这些演化网络可能存在一些特殊的性质.近年来,这些生灭网络受到了广泛的关注,大部分的生灭网络的研究都聚焦于度分布的求解和它们的性质.本文研究了节点增加概率0pmq;利用这些性质,运用生成函数法求解出不同网络规模的平均度的精确表达式;最后,采用数值模拟方法验证了平均度的精确求解结果和性质,讨论了平均度与节点增加概率p以及连接数m之间的关系.
    In the social and biological networks,each agent experiences a birth-and-death process.These evolving networks may exhibit some unique characteristics.Recently,the birth-and-death networks have gradually caught attention,and thus far,most of these studies on birth-and-death networks have focused on the calculations of the degree distributions and their properties.In this paper,a kind of random birth-and-death network (RBDN) with reducing network size is discussed,in which at each time step,with probability p(0pq=1-p.Unlike the existing literature,this study is to calculate the average degrees of the proposed networks under different network sizes.First,for the reducing RBDN,the steady state equations for each node's degree are given by using the Markov chain method based on stochastic process rule,and then the recursive equations of average degree for different network sizes are obtained according to these steady state equations.Second,by means of the recursive equations,we explore four basic properties of average degrees as follows:1) the average degrees are limited,2) the average degrees are strictly monotonically increasing,3) the average degrees are convergent to 2mq,and 4) the sum of each difference between the average degree and 2mq is a bounded number.Theoretical proofs for these four properties are also provided in this paper.Finally,on the basis of these properties,a generation function approach is employed to obtain the exact solutions of the average degrees for various network sizes.In addition to the theoretical derivations to the average degrees,computer simulation is also used to verify the correctness of exact solutions of the average degrees and their properties.Furthermore,we use numerical simulation to study the relationship between the average degree and node increasing probability p.Our simulation results show as follows:1) with the increasing of p,the convergent speed of the average degree to 2mq is increasing;2) with the increasing of m,the convergent speed of the average degree to 2mq is decreasing.In conclusion,for the proposed RBDN model,the main contributions of this study include 1) providing the recursive equations of the average degrees under different network sizes,2) investigating the basic properties for the average degrees,and 3) obtaining the exact solutions of the average degrees.
      通信作者: 张晓军, sczhxj@uestc.edu.cn
    • 基金项目: 国家自然科学基金(批准号:61273015)资助的课题.
      Corresponding author: Zhang Xiao-Jun, sczhxj@uestc.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61273015).
    [1]

    Adamic L A, Huberman B A, Barábasi A L, Albert R, Jeong H, Bianconi G 2000 Science 287 2115a

    [2]

    Watts D J, Strogatz S H 1998 Nature 393 440

    [3]

    Guimerà R, Arenas A, Díaz-Guilera A, Giralt F 2002 Phys. Rev. E 66 026704

    [4]

    Williams R J, Martinez N D 2000 Nature 404 180

    [5]

    Otto S B, Rall B C, Brose U 2007 Nature 450 1226

    [6]

    Dorogovtsev S N, Mendes J F F 2001 Phys. Rev. E 63 056125

    [7]

    Moreno Y, Gómez J B, Pacheco A F 2002 Europhys. Lett. 58 630

    [8]

    Sarshar N, Roychowdhury V 2004 Phys. Rev. E 69 026101

    [9]

    Slater J L, Hughes B D, Landman K A 2006 Phys. Rev. E 73 066111

    [10]

    Moore C, Ghoshal G, Newman M E J 2006 Phys. Rev. E 74 036121

    [11]

    Farid N, Christensen K 2006 New. J. Phys. 8 212

    [12]

    Saldaña J 2007 Phys. Rev. E 75 027102

    [13]

    Ben-Naim E, Krapivsky P L 2007 J. Phys. A 40 8607

    [14]

    Cai K Y, Dong Z, Liu K, Wu X Y 2011 Stoch. Proc. Appl. 121 885

    [15]

    Zhang X J, He Z, Rayman-Bacchus L 2016 J. Stat. Phys. 162 842

    [16]

    Zhang X J, Yang H L 2016 Chin. Phys. B 25 060202

    [17]

    Barabási A L, Albert R, Jeong H 1999 Physica A 272 173

    [18]

    Krapivsky P L, Redner S, Leyvraz F 2000 Phys. Rev. Lett. 85 4629

    [19]

    Dorogovtsev S N, Mendes J F F, Samukhin A N 2000 Phys. Rev. Lett. 85 4633

    [20]

    Dorogovtsev S N 2003 Phys. Rev. E 67 045102

    [21]

    Krapivsky P L, Redner S 2002 J. Phys. A 35 9517

    [22]

    Shi D H, Chen Q H, Liu L M 2005 Phys. Rev. E 71 036140

    [23]

    Zheng J F, Gao Z Y, Zhao H 2007 Physica A 376 719

    [24]

    Zhang X J, He Z S, He Z, Lez R B 2012 Physica A 391 3350

    [25]

    Tang L, Wang B 2010 Physica A 389 2147

    [26]

    Smith D M D, Onnela J P, Jones N S 2009 Phys. Rev. E 79 056101

    [27]

    Ferretti L, Cortelezzi M 2011 Phys. Rev. E 84 016103

    [28]

    Wang Y Q, Wang J, Yang H B 2014 Acta Phys. Sin. 63 208902 (in Chinese)[王亚奇, 王静, 杨海滨2014物理学报63 208902]

    [29]

    Yu X P, Pei T 2013 Acta Phys. Sin. 62 208901(in Chinese)[余晓平, 裴韬2013物理学报62 208901]

  • [1]

    Adamic L A, Huberman B A, Barábasi A L, Albert R, Jeong H, Bianconi G 2000 Science 287 2115a

    [2]

    Watts D J, Strogatz S H 1998 Nature 393 440

    [3]

    Guimerà R, Arenas A, Díaz-Guilera A, Giralt F 2002 Phys. Rev. E 66 026704

    [4]

    Williams R J, Martinez N D 2000 Nature 404 180

    [5]

    Otto S B, Rall B C, Brose U 2007 Nature 450 1226

    [6]

    Dorogovtsev S N, Mendes J F F 2001 Phys. Rev. E 63 056125

    [7]

    Moreno Y, Gómez J B, Pacheco A F 2002 Europhys. Lett. 58 630

    [8]

    Sarshar N, Roychowdhury V 2004 Phys. Rev. E 69 026101

    [9]

    Slater J L, Hughes B D, Landman K A 2006 Phys. Rev. E 73 066111

    [10]

    Moore C, Ghoshal G, Newman M E J 2006 Phys. Rev. E 74 036121

    [11]

    Farid N, Christensen K 2006 New. J. Phys. 8 212

    [12]

    Saldaña J 2007 Phys. Rev. E 75 027102

    [13]

    Ben-Naim E, Krapivsky P L 2007 J. Phys. A 40 8607

    [14]

    Cai K Y, Dong Z, Liu K, Wu X Y 2011 Stoch. Proc. Appl. 121 885

    [15]

    Zhang X J, He Z, Rayman-Bacchus L 2016 J. Stat. Phys. 162 842

    [16]

    Zhang X J, Yang H L 2016 Chin. Phys. B 25 060202

    [17]

    Barabási A L, Albert R, Jeong H 1999 Physica A 272 173

    [18]

    Krapivsky P L, Redner S, Leyvraz F 2000 Phys. Rev. Lett. 85 4629

    [19]

    Dorogovtsev S N, Mendes J F F, Samukhin A N 2000 Phys. Rev. Lett. 85 4633

    [20]

    Dorogovtsev S N 2003 Phys. Rev. E 67 045102

    [21]

    Krapivsky P L, Redner S 2002 J. Phys. A 35 9517

    [22]

    Shi D H, Chen Q H, Liu L M 2005 Phys. Rev. E 71 036140

    [23]

    Zheng J F, Gao Z Y, Zhao H 2007 Physica A 376 719

    [24]

    Zhang X J, He Z S, He Z, Lez R B 2012 Physica A 391 3350

    [25]

    Tang L, Wang B 2010 Physica A 389 2147

    [26]

    Smith D M D, Onnela J P, Jones N S 2009 Phys. Rev. E 79 056101

    [27]

    Ferretti L, Cortelezzi M 2011 Phys. Rev. E 84 016103

    [28]

    Wang Y Q, Wang J, Yang H B 2014 Acta Phys. Sin. 63 208902 (in Chinese)[王亚奇, 王静, 杨海滨2014物理学报63 208902]

    [29]

    Yu X P, Pei T 2013 Acta Phys. Sin. 62 208901(in Chinese)[余晓平, 裴韬2013物理学报62 208901]

  • [1] 隋怡晖, 郭星奕, 郁钧瑾, Alexander A. Solovev, 他得安, 许凯亮. 生成对抗网络加速超分辨率超声定位显微成像方法研究. 物理学报, 2022, 71(22): 224301. doi: 10.7498/aps.71.20220954
    [2] 阮逸润, 老松杨, 汤俊, 白亮, 郭延明. 基于引力方法的复杂网络节点重要度评估方法. 物理学报, 2022, 71(17): 176401. doi: 10.7498/aps.71.20220565
    [3] 唐国智, 汪垒, 李顶根. 使用条件生成对抗网络生成预定导热率多孔介质. 物理学报, 2021, 70(5): 054401. doi: 10.7498/aps.70.20201061
    [4] 胡炜, 廖建彬, 杜永乾. 一种适用于大规模忆阻网络的忆阻器单元解析建模策略. 物理学报, 2021, 70(17): 178505. doi: 10.7498/aps.70.20210116
    [5] 阮逸润, 老松杨, 王竣德, 白亮, 陈立栋. 基于领域相似度的复杂网络节点重要度评估算法. 物理学报, 2017, 66(3): 038902. doi: 10.7498/aps.66.038902
    [6] 魏德志, 陈福集, 郑小雪. 基于混沌理论和改进径向基函数神经网络的网络舆情预测方法. 物理学报, 2015, 64(11): 110503. doi: 10.7498/aps.64.110503
    [7] 胡耀光, 王圣军, 金涛, 屈世显. 度关联无标度网络上的有倾向随机行走. 物理学报, 2015, 64(2): 028901. doi: 10.7498/aps.64.028901
    [8] 韩华, 吴翎燕, 宋宁宁. 基于随机矩阵的金融网络模型. 物理学报, 2014, 63(13): 138901. doi: 10.7498/aps.63.138901
    [9] 吴腾飞, 周昌乐, 王小华, 黄孝喜, 谌志群, 王荣波. 基于平均场理论的微博传播网络模型. 物理学报, 2014, 63(24): 240501. doi: 10.7498/aps.63.240501
    [10] 刘金良. 具有随机节点结构的复杂网络同步研究. 物理学报, 2013, 62(4): 040503. doi: 10.7498/aps.62.040503
    [11] 余晓平, 裴韬. 手机通话网络度特征分析. 物理学报, 2013, 62(20): 208901. doi: 10.7498/aps.62.208901
    [12] 于海涛, 王江, 刘晨, 车艳秋, 邓斌, 魏熙乐. 耦合小世界神经网络的随机共振. 物理学报, 2012, 61(6): 068702. doi: 10.7498/aps.61.068702
    [13] 周漩, 张凤鸣, 李克武, 惠晓滨, 吴虎胜. 利用重要度评价矩阵确定复杂网络关键节点. 物理学报, 2012, 61(5): 050201. doi: 10.7498/aps.61.050201
    [14] 钭斐玲, 胡延庆, 黎勇, 樊瑛, 狄增如. 空间网络上的随机游走. 物理学报, 2012, 61(17): 178901. doi: 10.7498/aps.61.178901
    [15] 邢长明, 刘方爱, 徐如志. 无标度立体Koch网络上随机游走的平均吸收时间. 物理学报, 2012, 61(20): 200503. doi: 10.7498/aps.61.200503
    [16] 吕翎, 邹家蕊, 杨明, 孟乐, 郭丽, 柴元. 大规模富社团网络的时空混沌同步. 物理学报, 2010, 59(10): 6864-6870. doi: 10.7498/aps.59.6864
    [17] 赵清贵, 孔祥星, 侯振挺. 简易广义合作网络度分布的稳定性. 物理学报, 2009, 58(10): 6682-6685. doi: 10.7498/aps.58.6682
    [18] 刘光杰, 单 梁, 戴跃伟, 孙金生, 王执铨. 基于混沌神经网络的单向Hash函数. 物理学报, 2006, 55(11): 5688-5693. doi: 10.7498/aps.55.5688
    [19] 孟续军, 孙永盛, 李世昌. 原子平均离化度的研究. 物理学报, 1994, 43(3): 345-350. doi: 10.7498/aps.43.345
    [20] 蔡金涛. 电网络行列式展开之简捷法. 物理学报, 1939, 3(2): 148-181. doi: 10.7498/aps.3.148
计量
  • 文章访问数:  4745
  • PDF下载量:  266
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-05-28
  • 修回日期:  2016-06-30
  • 刊出日期:  2016-12-05

/

返回文章
返回