一种信息传播促进网络增长的网络演化模型

刘树新; 季新生; 刘彩霞; 郭虹

doi:10.7498/aps.63.158902

摘要

为了研究信息传播过程对复杂网络结构演化的影响，提出了一种信息传播促进网络增长的网络演化模型，模型包括信息传播促进网内增边、新节点通过局域世界建立第一条边和信息传播促进新节点连边三个阶段，通过多次自回避随机游走模拟信息传播过程，节点根据路径节点的节点度和距离与其选择性建立连接。理论分析和仿真实验表明，模型不仅具有小世界和无标度特性，而且不同参数下具有漂移幂律分布、广延指数分布等分布特性，呈现小变量饱和、指数截断等非幂律现象，同时，模型可在不改变度分布的情况下调节集聚系数，并能够产生从同配到异配具有不同匹配模式的网络.

关键词:

Abstract

In many real complex networks, information transmission occurs all the time. To study the effects of information transmission on the complex network evolution, we propose a new model for network growth promoted by the information transmission. The model includes three major steps: (i) New links attached to the nodes on the information transmission path, whose source point is chosen preferentially; (ii) the first link of the new node attached to the nodes in the local-world; (iii) other links of the new node attached to the nodes on the information transmission path, whose source point is the new node. The process of information transmission is simulated by self-avoiding random walk, and by considering the local information including its degree and distance; selective connection is established between the nodes on the information transmission path. Theoretical analysis and numerical simulation results show that the proposed model can not only reproduce small-world and scale-free network characteristics, but also indicate that shift power-law distribution and truncated power law function may form for different parameters which have some non-power-law features, such as exponential cutoff, and saturation for small variables. Moreover, in our model, the clustering coefficient is tunable without changing the degree distribution, and the model can also construct a network with assortative or disassortative mixed pattern.

Keywords:

作者及机构信息

1.
国家数字交换系统工程技术研究中心, 郑州 450002;

2.
信息工程大学信息系统工程学院, 郑州 450002

基金项目: 国家高技术研究发展计划（批准号：2011AA010605，2011AA010604）资助的课题.

Authors and contacts

1.
National Digital Switching System Engineering and Technological R&D Center, Zhengzhou 450002, China;

2.
Institute of Information System Engineering, Information Engineering University of PLA, Zhengzhou 450002, China

Funds: Project supported by the National High Technology Research and Development Program of China (Grant Nos. 2011AA010605, 2011AA010604).

参考文献

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施引文献

[1]	Erdös P, Rényi A 1960 Publ. Math. Inst. Hungar. Acad. Sci. 5 17
[2]
[3]
[4]	Watts D J, Strogatz S H 1998 Nature 393 440
[5]
[6]	Barabási A L, Albert R 1999 Science 286 509
[7]
[8]	Fang J Q, Wang X F, Zheng Z G, Bi Q, Di Z R, Li X 2007 Prog. Phys. 27 239 (in Chinese) [方锦清, 汪小帆, 郑志刚, 毕桥, 狄增如, 李翔 2007 物理学进展 27 239]
[9]
[10]	Cui A X, Fu Y, Shang M S, Chen D B, Zhou T 2011 Acta Phys. Sin. 60 38901 (in Chinese) [崔爱香, 傅彦, 尚明生, 陈端兵, 周涛 2011 60 38901]
[11]
[12]	Li M, Zou H, Guan S, Gong X, Li K, Di Z, Lai C H 2013 Sci. Rep. 3 2512
[13]	Jeong H, Mason S P, Barabási A L, Oltvai Z N 2001 Nature 1 41
[14]
[15]	Amaral L A N, Scala A, Barthelemy M, Stanley H E 2000 Proc. Natl. Acad. Sci. USA 97 11149
[16]
[17]
[18]	Li S M, Xu X H, Meng L H 2012 Chin. Phys. B 21 088901
[19]	Zhou T, Han X P, Yan X Y, Yang Z M, Zhao Z D, Wang B H 2013 Journal of University of Electronic Science and Technology of China 42 482 (in Chinese) [周涛, 韩筱璞, 闫小勇, 杨紫陌, 赵志丹, 汪秉宏 2013 电子科技大学学报 42 482]
[20]
[21]
[22]	Zhao Z D, Yang Z, Zhang Z, Zhou T, Huang Z G, Lai Y C 2013 Sci. Rep. 3 3472
[23]
[24]	Lü L, Zhou T 2011 Physica A 390 1150
[25]	Wang B H, Zhou T, Zhou C S 2012 Journal of University of Shanghai for Science and Technology 34 103 (in Chinese) [汪秉宏, 周涛, 周昌松 2012 上海理工大学学报 34 103]
[26]
[27]
[28]	Yang C L, Tang K S 2011 Chin. Phys. B 20 128901
[29]	Chen G R 2013 Acta Autom. Sin. 39 312 (in Chinese) [陈关荣 2013 自动化学报 39 312]
[30]
[31]
[32]	Liu Y Y, Slotine J J, Barabási A L 2013 Proc. Natl. Acad. Sci. USA 110 2460
[33]
[34]	Albert R, Barabási A L 2000 Phys. Rev. Lett. 85 5234
[35]	Bianconi G, Barabási A L 2001 Phys. Rev. Lett. 86 5632
[36]
[37]
[38]	Holme P, Kim B J 2002 Phys. Rev. 65 026107
[39]	Li X, Chen G 2003 Physica A 328 274
[40]
[41]
[42]	Wang G Z, Cao Y J, Bao Z J, Han Z X 2009 Acta Phys. Sin. 58 3597 (in Chinese) [王光增, 曹一家, 包哲静, 韩祯祥 2009 58 3597]
[43]
[44]	Yuan S Q, Zhao H, Li C, Zhang X 2008 Acta Phys. Sin. 57 4805 (in Chinese) [袁韶谦, 赵海, 李超, 张昕 2008 57 4805]
[45]
[46]	Wang L N, Guo J L, Yang H X, Zhou T 2009 Physica A 388 1713
[47]
[48]	Jiang Z H, Wang H, Gao C 2011 Acta Phys. Sin. 60 58903 (in Chinese) [姜志宏, 王晖, 高超 2011 60 58903]
[49]
[50]	Saramäki J, Kaski K 2004 Physica A 341 80
[51]
[52]	Zhu C P, Zhou T, Yang H J, Xiong S J, Gu Z M, Shi D N, He D R, Wang B H 2008 New J. Phys. 10 023006
[53]
[54]	Zhang P P, He Y, Zhou T, Su B B, Chang H, Zhou Y P, Wang B H, He D R 2006 Acta Phys. Sin. 55 60 (in Chinese) [张培培, 何阅, 周涛, 苏蓓蓓, 常慧, 周月平, 汪秉宏, 何大韧 2006 55 60]
[55]
[56]	Wang X F, Chen G R 2006 Complex Networks Theory and its Applications (Beijing: Tsinghua University Press) (in Chinese) [汪小帆, 李翔, 陈关荣2006复杂网络理论及其应用(北京: 清华大学出版社)]
[57]	Chang H, Su B B, Zhou Y P, He D R 2007 Physica A 383 687
[58]
[59]	Bornholdt S, Schuster H G 2003 Handbook of graphs and networks (New York: Wiley-Vch) pp318
[60]
[61]
[62]	Noh J D, Rieger H 2004 Phys. Rev. Lett. 92 118701
[63]
[64]	Herrero C P, Saboyá M 2003 Phys. Rev. E 68 026106
[65]	Bar S, Gonen M, Wool A 2004 An incremental super-linear preferential Internet topology model (Berlin: Springer-Heidelberg) pp53-62
[66]
[67]	Li Y, Fang J Q, Liu Q 2007 Science & Technology Review 25 23 (in Chinese) [李永, 方锦清, 刘强 2007 科技导报 25 23]
[68]
[69]
[70]	Jost J, Joy M P 2002 Phys. Rev. E 66 036126
[71]	Cao Y J, Wang G Z, Jiang Q Y, Han Z X 2006 Phys. Lett. A 349 462
[72]
[73]
[74]	Yang X H, Lou S L, Chen G, Chen S Y, Huang W 2013 Physica A 392 3531
[75]	Newman M E J 2003 SIAM review 45 167
[76]
[77]	Wang X F, Chen G 2003 IEEE Circuits and Systems Magazine 3 6
[78]
[79]	Newman M E J 2003 Phys. Rev. Lett. 89 208701

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