计算机应用   2017, Vol. 37 Issue (4): 1083-1087  DOI: 10.11772/j.issn.1001-9081.2017.04.1083 0

### 引用本文

ZHANG Yanan, SUN Shibao, ZHANG Jingshan, YIN Lihang, YAN Xiaolong. Opinion formation model of social network based on node intimacy and influence[J]. Journal of Computer Applications, 2017, 37(4): 1083-1087. DOI: 10.11772/j.issn.1001-9081.2017.04.1083.

### 文章历史

Opinion formation model of social network based on node intimacy and influence
ZHANG Yanan, SUN Shibao, ZHANG Jingshan, YIN Lihang, YAN Xiaolong
College of Information Engineering, Henan University of Science & Technology, Luoyang Henan 471023, China
Abstract: Aiming at the universality of individual interaction and the heterogeneity of individual social influence in opinion spreading, an opinion formation model of social network was proposed on the basis of Hegselmann-Krause model. By introducing the concepts of intimacy between individuals, interpersonal similarity and interaction strength, the individual interactive set was extended, the influence weight was reasonably quantified, and more realistic view of interaction rule was built. Through a series of simulation experiments, the effects of main parameters in the model on opinion evolution were analyzed. The simulation results indicate that group views can converge to the same and form consensus under different confidence thresholds. And the larger the confidence threshold is, the shorter the convergence time is. When confidence threshold is 0.2, convergence time is only 10. Meanwhile, extending the interactive set and increasing the strength of interpersonal similarity will promote consensus formation. Besides, when the clustering coefficient and the average degree of scale-free network are higher, the group views are more likely to produce convergence effect. The results are helpful to understand the dynamic process of opinion formation, and can guide social managers to make decisions and analysis.
Key words: social network    opinion formation    consensus    intimacy    interpersonal similarity    interaction strength
0 引言

1 网络模型

 图 1 度分布图 (m0=20, pt=0.8) Figure 1 Degree distribution (m0=20, pt=0.8)
2 舆论形成模型

2.1 计算交互集合

 ${c_{ij}} = {e^{1 - {d_{ij}}}}$ (1)

1) 按照有界信任算法选择与i的观点差距处于信任阈值ε内的个体集合, 即:

 $N{\rm{ei}}ghbor_{i,1}^t = \{ j \in A|\mu _{ij}^t \le \varepsilon ,j \ne i\}$ (2)

2) 根据“亲密度原则”选择m个信任阈值外的随机节点作为交互对象。如果个体j的观点在i的信任阈值外, 那么ji选为阈值外交互对象的概率可表述为pijt, 如式 (3) 所示：

 $p_{i,j}^t = \frac{{{e^{\lambda {c_{ij}}}}}}{{\sum\limits_{k \notin Neighbor_{i,1}^t \cup \{ i\} } {{e^{\lambda {c_{ik}}}}} }}$ (3)

 $Neighbor_i^t = N{\rm{ei}}ghbor_{i,1}^t \cup N{\rm{ei}}ghbor_{i,2}^t$ (4)
2.2 观点更新规则

 $o_i^{t + 1} = \frac{1}{{|Neighbor_{i,1}^t|}}\sum\limits_{j \in Neighbor_{i,1}^t} {o_j^t}$ (5)

 $S_{i,j}^t = \frac{{|\mathit{\pmb{\Gamma}} (i) \cap \mathit{\pmb{\Gamma}} (j)|}}{{\sqrt {k(i) \times k(j)} }}$ (6)

 $E_{i,j}^t = \frac{{\mathit{\pmb{\Psi}} (i,j)}}{{\sqrt {\mathit{\pmb{\Psi}} (i) \times \mathit{\pmb{\Psi}} (j)} }}$ (7)

 $I_{i,j}^t = \alpha S_{i,j}^t + \left( {1 - \alpha } \right)E_{i,j}^t$ (8)

 $w_{ij}^t{\rm{ = }}\left\{ {\begin{array}{*{20}{l}} {\frac{{I_{i,j}^t}}{{\sum\limits_{r \in Neighbor_i^t} {I_{i,r}^t} }}{\rm{, }}j \in Neighbor_i^t}\\ {{\rm{ }}0{\rm{ }},\;\;\;\;{\rm{ 其他}}} \end{array}} \right.$ (9)

t+1时刻, 所有个体同步更新观点:将交互集合内个体观点的加权平均值作为该时刻个体的观点值, 如式 (10) 所示：

 ${{\boldsymbol{O}}^{t{\boldsymbol{ + }}1}}{\boldsymbol{ = }}{{\boldsymbol{W}}^{t{\boldsymbol{ + }}1}}{{\boldsymbol{O}}^t}$ (10)

 $o_{{\rm{max}}}^t - o_{{\rm{min}}}^t \le \xi$ (11)

3 实验与分析

3.1 舆论共识的形成

 图 2 经典HK模型中不同ε下群体观点的收敛过程 Figure 2 Convergence process of group views under different ε in classical HK model
 图 3 新模型中不同ε下群体观点的收敛过程 (λ=0, m=5) Figure 3 Convergence process of group views under different ε in the new model (λ=0, m=5)
 图 4 新模型中不同ε下参数λ、m与收敛时间CT的关系 Figure 4 Relationship among parameters λ, m and convergence time CT under different ε in the new model

3.2 影响力构成因素中α对舆论形成的影响

 图 5 影响力构成因素对舆情形成的影响 Figure 5 Influence of influential factors on the formation of public opinion

3.3 网络结构特征对舆论形成的影响

3.2节讨论了影响力构成因素与收敛时间的关系, 粗略得出提高人际相似性的作用强度有利于舆论收敛。而决定人际相似性的关键因素则是网络节点度数和节点间共同邻居数量 (式 (6))。因此本节尝试从平均度Degree和聚类系数Cluster的角度进一步探讨网络结构特征在舆论形成中的作用。首先令N=1 000, m0∈{5, 10, 15}, pt∈[0, 1], 根据第1章中的算法分别生成Degree∈{10, 20, 30}的三个可变聚类系数网络; 再固定ε=0.01, λ=0, m=5, α=0.5不变, 进行仿真实验, 所得结果如图 6所示。

 图 6 不同pt条件下舆论收敛时间CT的变化 Figure 6 Variation of convergence time CT under different probability pt

4 结语

 [1] SZNAJD-WERON K, SZNAJD J. Opinion evolution in closed community[J]. International Journal of Modern Physics C, 2000, 11 (6) : 1157-1165. doi: 10.1142/S0129183100000936 [2] GRABOWSKI A, KOSINSKI R A. Ising-based model of opinion formation in a complex network of interpersonal interactions[J]. Physica A: Statistical Mechanics and its Applications, 2006, 361 (2) : 651-664. doi: 10.1016/j.physa.2005.06.102 [3] DEFFUANT G, NEAU D, AMBLARD F, et al. Mixing beliefs among interacting Agents[J]. Advances in Complex System, 2000, 3 (01n04) : 87-98. doi: 10.1142/S0219525900000078 [4] HEGSELMANN R, KRAUSE U. Opinion dynamics and bounded confidence: models, analysis and simulation[J]. Journal of Artificial Societies and Social Simulation, 2002, 5 (3) : 1-24. [5] LI H, LI Z, WU Y, et al. An improved evolutionary model of public opinion based on KH model and BA scale-free network[J]. Journal of Information and Computational Science, 2013, 10 (12) : 3939-3955. doi: 10.12733/issn.1548-7741 [6] SU J, LIU B, LI Q, et al. Coevolution of opinions and directed adaptive networks in a social group[J]. Journal of Artificial Societies and Social Simulation, 2014, 17 (2) : 4. doi: 10.18564/jasss.2424 [7] CHEN S, GLASS D H, MCCARTNEY M. Characteristics of successful opinion leaders in a bounded confidence model[J]. Physica A: Statistical Mechanics and its Applications, 2016, 449 : 426-436. doi: 10.1016/j.physa.2015.12.107 [8] 赵奕奕, 彭怡, 肖磊, 等. 突发事件下群体抢购行为的舆论传播机理研究[J]. 系统工程理论与实践, 2015, 35 (3) : 616-622. ( ZHAO Y Y, PENG Y, XIAO L, et al. On opinion propagation mechanism of collective panic buying under emergences[J]. System Engineering-Theory & Practice, 2015, 35 (3) : 616-622. ) [9] LIU Q, WANG X. Opinion dynamics with similarity-based random neighbors[J]. Scientific Reports, 2013, 3 (10) : 2968. [10] WANG H, SHANG L. Opinion dynamics in networks with common-neighbors-based connections[J]. Physica A: Statistical Mechanics and its Applications, 2015, 421 : 180-186. doi: 10.1016/j.physa.2014.10.090 [11] 徐恪, 张赛, 陈昊, 等. 在线社会网络的测量与分析[J]. 计算机学报, 2014, 37 (1) : 165-188. ( XU K, ZHANG S, CHEN H, et al. Measurement and analysis of online social networks[J]. Chinese Journal of Computers, 2014, 37 (1) : 165-188. ) [12] GHOSH S, GANGULY N. Social Networking[M]. Berlin: Spring International Publishing, 2014 : 23 -44. [13] HOLME P, KIM B J. Growing scale-free networks with tunable clustering[J]. Physical Review E, 2002, 65 (2) : 95-129.