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在线社会网络中，信息传播蕴含着复杂的动力学成因.本文将传染病模型与社交影响力要素相结合，并针对影响力度量中主要研究静态网络拓扑结构、忽略个体行为特征的问题，提出一种基于动态节点行为和用户影响力的信息传播动力学模型，旨在量化影响力强度，为研究信息扩散过程中不同用户群体状态转变提供理论依据.首先，在网络拓扑结构和用户行为两方面，提取个人记忆和用户交互两个表征，分析影响力形成的内因和外因两个动力学成因，并基于多元线性回归模型，提出一种度量用户社会影响力的方法.其次，在传统传染病SIR（susceptible-infected-recovered）模型基础上，结合信息扩散与传染病蔓延相似的传播机理，综合考虑信息传播的多源并发性和双向性，引入影响力因子，利用平均场理论改进得到一种基于用户影响力的信息传播模型.实验表明，该模型能有效地解释在线社会网络中信息传播的动力学原因，感知社会网络中信息传播演化态势.With the development of online social networks, they rapidly become an ideal platform for information about social information diffusion, commodity marketing, shopping recommendation, opinion expression and social consensus. The social network information propagation has become a research hotspot correspondingly. Meanwhile, information diffusion contains complex dynamic genesis in online social networks. In view of the diversity of information transmission, the efficiency of propagation and the convenience of interaction, it is very important to regulate the accuracy, strengthen the public opinion monitoring and formulating the information control strategy. The purpose of this study is to quantify the intensity of the influence, especially provides a theoretical basis for studying the state transition of different user groups in the evolution process. As existing epidemic model paid less attention to influence factors and previous research about influence calculation mainly focused on static network topology but ignored individual behavior characteristics, we propose an information diffusion dynamics model based on dynamic user behaviors and influence. Firstly, according to the multiple linear regression model, we put forward a method to analyze internal and external factors for influence formation from two aspects:personal memory and user interaction. Secondly, for a similar propagation mechanism of information diffusion and epidemics spreading, in this paper we present an improved SIR model based on mean-field theory by introducing influence factor. The contribution of this paper can be summarized as follows. 1) For the influence quantification, different from the current research work that mainly focuses on network structure, we integrate the internal factors and external factors, and propose a user influence evaluation method based on the multiple linear regression model. The individual memory principle is analyzed by combining user attributes and individual behavior. User interaction is also studied by using the shortest path method in graph theory. 2) On modeling the information diffusion, by referring SIR model, we introduce the user influence factor as the parameter of the state change into the epidemic model. The mean-field theory is used to establish the differential equations. Subsequently, the novel information diffusion dynamics model and verification method are proposed. The method avoids the randomness of the artificial setting parameters within the model, and reveals the nature of multi-factors coupling in the information transmission. Experimental results show that the optimized model can comprehend the principle and information diffusion mechanism of social influence from a more macroscopic level. The study can not only explain the internal and external dynamics genesis of information diffusion, but also explore the behavioral characteristics and behavior laws of human. In addition, we try to provide theoretical basis for situation awareness and control strategy of social information diffusion.
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[1] Cai M, Du H F, Feldman M W 2014 Acta Phys. Sin. 63 060504 (in Chinese)[蔡萌, 杜海峰, Feldman M W 2014 63 060504]
[2] Zhou B, He Z, Jiang L L, Wang N X, Wang B H 2014 Sci. Rep. 4 7577
[3] Huang J, Li C, Wang W Q, Shen H W, Li G, Cheng X Q 2014 Sci. Rep. 4 5334
[4] Zheng M, L L, Zhao M 2013 Phys. Rev. E 88 012818
[5] Chen D B, Huang S, Shang M S 2011 Comput. Sci. 38 118 (in Chinese)[陈端兵, 黄晟, 尚明生2011计算机科学38 118]
[6] Chen D B, Gao H 2012 Chin. Phys. Lett. 29 048901
[7] Borge-Holthoefer J, Moreno Y 2012 Phys. Rev. E 85 026116
[8] Wang C, Liu C Y, Hu Y P, Liu Z H, Ma J F 2014 Acta Phys. Sin. 63 180501 (in Chinese)[王超, 刘骋远, 胡远萍, 刘志宏, 马建峰2014 63 180501]
[9] Lu W, Chen W, Lakshmanan L V S 2015 Proceedings of the VLDB Endowment Hawaii, USA, August 31-September 4, 2015 p60
[10] Elias Boutros K, Dilkina B, Song L 2014 Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining New York, USA, August 24-27, 2014 p1226
[11] Singer Y 2012 Proceedings of the Fifth ACM International Conference on Web Search and Data Mining Washington, USA, February 8-12, 2012 p733
[12] Liu J G, Lin J H, Guo Q, Zhou T 2016 Sci. Rep. 6 21380
[13] Montanari A, Saberi A 2010 Proc. Natl. Acad. Sci. 107 20196
[14] Yuan X P, Xue Y K, Liu M X 2013 Chin. Phys. B 22 030207
[15] Pastor-Satorras R, Castellano C, van Mieghe P, Vespignani A 2015 Rev. Mod. Phys. 87 925
[16] Kempe D, Jon K, Éva T 2003 Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining Washington, USA, August 24-27, 2003 p137
[17] Liu Q M, Deng C S, Sun M C 2014 Physica A 410 79
[18] Li C H, Tsai C C, Yang S Y 2014 Commun. Nonlinear Sci. 19 1042
[19] Chen L, Sun J 2014 Physica A 410 196
[20] Xiong F, Liu Y, Zhang Z J, Zhu J, Zhang Y 2012 Phys. Lett. A 376 2103
[21] Li T, Wang Y, Guan Z H 2014 Commun. Nonlinear Sci. 19 686
[22] Xiong F, Wang X M, Cheng J J 2016 Chin. Phys. B 25 108904
[23] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888
[24] Hu Q C, Zhang Y, Xu X H, Xing C X, Chen C, Chen X H 2015 Acta Phys. Sin. 64 190101 (in Chinese)[胡庆成, 张勇, 许信辉, 邢春晓, 陈池, 陈信欢2015 64 190101]
[25] L L Y, Chen D B, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016 Phys. Rep. 650 1
[26] Wu Y, Yang Y, Jiang F, Jin S, Xu J 2014 Physica A 416 467
[27] Liben-Nowell D, Kleinberg J 2008 Proc. Natl. Acad. Sci. 105 4633
[28] L L Y, Zhou T, Zhang Q M, Stanley H E 2016 Nat. Commun. 7 10168
[29] Myers S A, Zhu C, Leskovec J 2012 Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining Beijing, China, August 12-16, 2012 p33
[30] Aral S, Walker D 2012 Science 337 337
[31] La Fond T, Neville J 2010 Proceedings of the 19th International Conference on World Wide Web Raleigh, USA, April 26-30, 2010 p601
[32] Li P, Zhang J, Xu X K, Small M 2012 Chin. Phys. Lett. 29 048903
[33] Newman, M E J 2012 Nat. Phys. 8 25
[34] Barabási A L, Albert R, Jeong H 1999 Physica A 272 173
[35] Pedroche F, Moreno F, González A, Valencia A 2013 Math. Comput. Model 57 1891
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