MarkZ

Fw:TCSS-2024-07-0793-Revision1

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Comments 78

References 10

Rev.1

Accept as Regular Paper

Comment

  • 为什么在影响力探索中不考虑~~~~点赞~~~~的情况？

Thank you for your insightful comments and for drawing attention to the consideration of likes in the exploration of influence within social media contexts.

We acknowledge the importance of likes as a form of user engagement; however, our decision to focus on retweets (or shares) rather than likes was driven by the following rationale:

  1. Consciousness of Action: Unlike retweets, which actively disseminate content to one’s own network and thus imply a higher level of engagement and endorsement, likes can often be a more passive and spontaneous reaction. They may not necessarily reflect a deliberate decision to support or propagate the content in question.
  2. Intent and Emotion: We posit that the act of retweeting involves a more intentional and emotional response to the content. It suggests that the user not only appreciates the content but also finds it significant enough to share with their followers, thereby indicating a deeper level of influence.
  3. Accuracy in Content Dissemination: Retweets provide a more accurate metric for the spread of specific narratives or topics. They directly contribute to the visibility and reach of the original message, making them a more reliable indicator of influence and propagation within the social media ecosystem.
  4. Subconscious Likes: It is not uncommon for users to like content without a deliberate thought process, possibly due to habitual behavior or even as a means of social reciprocity. This can lead to a distortion of the true impact or influence a piece of content may hold.
  5. Data representativeness: While likes are undoubtedly a significant engagement metric, their inclusion in our analysis may have introduced noise that could obscure the more substantive interactions, such as retweets, which are more representative of the dissemination of ideas and the influence of the content.
  • 2. 用于识别负面和正面意见的模型有区别吗？影响力指标的构建上是否存在差异？特别是，对于负面舆论的识别，是否有更为详细的指标？

Rev.2

Prepare A Major Revision

Comment

  • 1. 现有研究的局限性没有清晰阐述，导致产生困惑。同时，文献综述不够全面，无法将研究有效地置于现有知识体系中。~~~~建议作者明确说明研究的局限性，并扩展文献综述，为研究提供更广泛的背景。

The limitations of existing research are not clearly articulated, which leads to confusion. There is also a perceived lack of comprehensive literature review to situate the study within the existing body of knowledge. It is recommended that the authors clarify the limitations and expand the literature review to provide a broader context for their work.

Thank you for your constructive feedback. I have thoroughly revised the introduction to clearly articulate the limitations of existing research and to situate the study within the broader context of relevant literature. This expanded literature review now provides a comprehensive foundation for our research, addressing the concerns about clarity and context. Thank you again for your valuable insights.

  • 2. 虽然关注者–被关注者比例的概念具有创新性，但似乎只是对更常见的出度/入度比例的重新命名，未体现出实质性创新。~~~~作者应解释这种新术语的必要性及其相较于现有衡量标准的优势。
  • 易于理解：关注者–被关注者比例这一术语更直观，尤其对于非技术背景的读者或用户而言，更容易理解和接受。相比之下，出度/入度比例虽然在学术上更为准确，但可能会让普通用户感到困惑。
  • 特定性：关注者–被关注者的表述形式广泛适用于社交媒体平台的用户体验和界面设计。所以，关注者–被关注者比例更专注于针对社交媒体中的关注关系，而出度/入度比例则是一个更广泛的图论概念，适用于各种网络结构分析。使用前者可以更明确地传达特定的社交媒体分析意图。

Thank you for your insightful comments regarding the terminology of the Followee–Follower Ratio.

● Ease of Understanding: The term “Followee–Follower Ratio” is more intuitive, particularly for readers or users without a technical background. It is accessible and more relatable for general audiences, whereas the out-degree/in-degree ratio, though academically precise, may be less comprehensible for non-technical users.

● Specificity: The Followee–Follower terminology aligns closely with user experience and interface design in social media platforms. This term is targeted specifically at the context of social media relationships, as opposed to the more general out-degree/in-degree ratio, which applies broadly in graph theory across various network structures. Using this term more clearly conveys the intent of social media analysis.

Thank you again for prompting these clarifications.

  • 3. 文章声称“最终构建的网络拓扑更准确地反映了网络特征”，但缺乏足够的证据支持这一结论。特别是，图1似乎无法证实这一论点。~~~~建议作者提供更详细的解释或额外的数据来支撑该说法~~~~。
  • 4. “通过多次模拟不同参数值的传播过程，并将结果与真实数据进行比较。”~~~~尚不清楚与真实数据（如帖子数量、舆论分布、领袖数量等）的哪个方面进行比较~~~~。同样，“验证模型与真实事件传播的高拟合度”这一表述也不清晰。~~~~作者应明确比较中使用的指标以及它们与现实数据的关系。

Thank you for your insightful comment.

1）Due to the improper organizational structure, the description was unclear. We have revised the original manuscript, placing this paragraph in a more prominent position to enhance clarity. In this study, we used post quantity as a proxy indicator for population size to facilitate comparison between the simulated spread and real-world data. For details, please see page 6, column 2, C. Data Acquisition and Processing.

To accurately capture and analyze the spread patterns of specific topics, considering that some topics span long periods and involve massive amounts of data, this paper selected the data focusing on the three consecutive days when each topic reached its peak popularity for in-depth statistical analysis. Additionally, based on the characteristic diurnal rhythm of human activity, which shows significant daytime activity and nighttime dormancy [48], we excluded nighttime data and chose the time window from 9 AM to 11 PM for statistical and analytical purposes to ensure the data reflects the substantial activities and core trends of topic spread.

Moreover, given the availability and ease of calculation of user behavior data on online platforms, we used data volume as a proxy for population size. Specifically, the proportion of information spread throughout the population is determined by the ratio of the data volume for the related topic to the overall total data volume. This method allows us to objectively infer engagement in social networks and assess the extent of information spread through digital traces [49].

2）We have overlooked this issue. For quantitative evaluation, we calculated the R² (coefficient of determination) to assess the degree of fit between the simulated spread results and real data. An R² close to 1 indicates a high fit between the model and real-world data. We have updated the manuscript to include these details.

Furthermore, this study quantitatively evaluates the curve fitting accuracy by comparing the coefficient of determination between the simulated and real data curves. In Figures (b), (c), and (d), the coefficients of determination are 0.9633, 0.8043, and 0.7724, respectively.

  • 5. 关于表III，~~~~未明确哪些参数来自蒙特卡洛模拟，哪些参数基于文献设定。~~~~建议作者清晰解释参数选择过程以及每个参数的选择依据。

感谢您对我们研究的宝贵意见。

  1. 抱歉，由于组织结构不清晰，导致您的疑惑。根据您的建议，现在已经修改了表 3，将表3拆分成了表 3 和表 4 .现在表 3 已经被修改到正确的位置。表 3 中，参数由德尔菲法确定。表4中，部分参数由蒙特卡洛模拟确定。

  2. We have revised the manuscript to include a detailed description of the Delphi method process used to determine the weights \omega_i, i \in {1, 2, 3, \dots, 6}. Specifically, we have clarified the selection criteria for experts and the multi-step process involved, including an open-ended survey, quantitative evaluation, and consensus refinement rounds. This iterative process ensured that expert opinions and the relative importance of each indicator were fully considered, resulting in a scientifically grounded evaluation system. Additionally, we have included the final parameter values in Table III for reference.

蒙特卡洛模拟参数

蒙特卡洛模拟参数是通过随机抽样方法生成的，用于模拟系统的不确定性和随机性。这些参数的选择基于以下步骤：

  1. 确定随机变量：识别系统中存在不确定性的关键变量。
  2. 选择分布类型：根据历史数据或领域专家的建议，选择适当的概率分布（如正态分布、均匀分布等）。
  3. 设定分布参数：通过统计分析或文献数据，确定分布的均值、方差等参数。
  • 6. 表III显示节点的度（包括出度和入度）在KOL识别中仍占据最高权重。~~~~作者应进行对比实验，展示多因素KOL识别方法相较于仅依赖网络结构方法的优势，并明确说明其方法的优点。

Thank you for the insightful feedback. In response, a supplementary experiment has been conducted to highlight the advantages of a multifactorial KOL (Key Opinion Leader) identification approach compared to a method that relies solely on network structure.

To demonstrate the advantages of a multifactorial KOL (Key Opinion Leader) identification approach over one that solely relies on network structure, this research did a supplementary experiment presents a comparative analysis of two methods for identifying opinion leaders: the Degree-Based method and the KOL Indicator-Based model, applied across four types of directed networks. These networks include an experimental network, a power grid network, a protein interaction network, and a real-world Weibo social network. Each method’s effectiveness is assessed by examining the proportion of identified opinion leader nodes within each network.

In Figure (a), the x-axis represents the network type, while the y-axis indicates the ratio of identified opinion leader nodes to the total number of nodes. Purple bars denote the Degree-Based approach, which identifies opinion leaders based solely on nodes with high in-degree and out-degree values (top \sigma% of nodes). Green bars represent the KOL Indicator-Based approach, which employs a multifactorial model to select the top \sigma% of Information Source nodes according to Algorithm 2.

Results show that the KOL Indicator-Based model consistently identifies a smaller, more targeted subset of opinion leader nodes than the Degree-Based method across all network types, including both social and non-social networks. Notably, in the real Weibo social network, the Degree-Based approach classifies over 20% of nodes as opinion leaders, whereas the KOL Indicator-Based model remains more selective and precise.

In Figure (b), the KOL Indicator-Based and Degree-Based approaches are compared in terms of negative guidance on the spread density under free propagation conditions, with real topic data as a reference. Both methods applied negative guidance at T=160. However, the Degree-Based approach failed to control the spread effectively post-intervention. Due to the overly broad and imprecise selection of opinion leader nodes, it actually amplified the spread, leading to an uncontrollable escalation of public opinion. In contrast, the KOL Indicator-Based approach demonstrated more targeted control, aligning more closely with real-case dynamics.

  • 7. 文章的第一句包含一个多~~~~余的单词“in”，~~~~应修正以提高清晰度。
  • 8. 文中有多处算法和表格的引用错误或缺失。例如，~~~~“Algorithm II-A”应为“Algorithm 1”；不存在“Table II-A”；文中未提到“表I”。

Reference

[1] Dong, Y., Ding, Z., Martínez, L., & Herrera, F. (2017). Managing consensus based on leadership in opinion dynamics. Information Sciences, 397, 187-205.
~~[2] Zhao, Y., Kou, G., Peng, Y., & Chen, Y. (2018). Understanding influence power of opinion leaders in e-commerce networks: An opinion dynamics theory perspective. Information Sciences, 426, 131-147.

~~[4] Bu, Z., Li, H. J., Zhang, C., Cao, J., Li, A., & Shi, Y. (2019). Graph K-means based on leader identification, dynamic game, and opinion dynamics. IEEE Transactions on Knowledge and Data Engineering, 32(7), 1348-1361. ~~
 
### Rev.3
 
Accept With Minor Changes
 
#### Comment
- [x] ~~1. 请在~~~~**第一页最后一段中提供该文章所填补的具体研究空白的列表**~~~~。~~
 
Thank you for your suggestion. I have provided a detailed list of the research gaps addressed in this article in the penultimate paragraph of the introduction. This addition clarifies the specific contributions of our study and highlights how it builds on and differentiates from existing research. I appreciate your valuable feedback!
 
- [x] ~~2. 作者是否关注了~~~~**影响网络舆论传播的具体因素**~~~~？~~
 
This study does address several specific factors that influence the spread of online public opinion, particularly the **role of opinion leaders** and the **dynamic changes in network topology**. The perspectives and emotional cues shared by opinion leaders can rapidly reach large audiences and play a crucial role in guiding the direction of public opinion. Additionally, the paper analyzes how network topology impacts the path and speed of information diffusion, especially as the social network evolves dynamically over time. However, broader influencing factors—such as content appeal and user interaction behaviors—are not covered in this study and would be valuable areas to explore in future research.
 
- [x] ~~3. 论文中确定~~~~**权重������ ����=(1,2,3,4,5,6)的科学性需要进一步讨论**~~~~。~~
 
Thank you for your valuable suggestion. We have revised the manuscript to include a detailed description of the Delphi method process used to determine the weights \omega_i, i \in \{1, 2, 3, \dots, 6\}. Specifically, we have clarified the selection criteria for experts and the multi-step process involved, including an open-ended survey, quantitative evaluation, and consensus refinement rounds. This iterative process ensured that expert opinions and the relative importance of each indicator were fully considered, resulting in a scientifically grounded evaluation system. Additionally, we have included the final parameter values in Table III for reference.
 
Due to the incommensurability of various indicators, this paper determines the weights ωi, i ∈ {1, 2, 3, . . .  , 6} using the Delphi method and conducts one-on-one interviews with experts (generally not exceeding 20).  The selected experts need to meet the following criteria: (i) expertise in public opinion control, (ii) availability, and (iii) willingness to par- ticipate in the Delphi panel [44].  The process included the following steps: 1) Open-ended Survey.  This round aimed to collect a broad range of views and establish a foundational understanding of expert opinions.  2) Quantitative Evaluation.  Based on feedback from Round 1, a structured questionnaire was designed, allowing experts to assign numerical weights to each indicator.  3) Consensus Refinement.  In this final round, experts were presented with the aggregated results from Round 2 and were encouraged to adjust their weights in light of the group’s feedback.  This iterative feedback loop continued until a consensus was reached on the weight values.  The opinions of the experts and the relative importance of the indicators are taken into account to ensure a scientific and reasonable evaluation system [45].  The parameters are shown in Table III.
 
- [x] ~~4. 在“关键意见领袖指标体系构建与传播机制”章节中的“C. KOL指标体系模型和舆论引导协同信息转发模型”部分。~~~~**本文与SI模型有何关联？**~~
 
In the section titled **"KOL Indicator System Model and Opinion Guidance Collaborative Information Forwarding Model,"** this paper builds on the **SI (Susceptible-Infected)** model framework by adapting it to the context of **Key Opinion Leaders (KOLs)** and their influence on public opinion spread in social networks. Specifically, the paper extends the SI model by incorporating **KOL-specific indicators**—such as influence, reach, and engagement—which capture the unique role of KOLs in shaping and amplifying public opinion. This extension is designed to reflect the dynamic of KOL-led information forwarding, where opinion leaders act as critical "infectious" nodes capable of influencing a large audience in a relatively short time.
 
The model applies SI principles by treating the audience as "susceptible" to influence when exposed to information spread by KOLs. Once influenced, these individuals can further propagate the information through their networks, creating a collaborative forwarding mechanism that aligns with SI-based spread dynamics but incorporates factors unique to KOL influence. This approach situates the traditional SI model within a social network framework focused on public opinion dynamics driven by KOLs.
 
- [x] ~~5. 关于网络舆论传播的研究，请参考文献10.1007/s11071-023-09021-5。关于谣言传播控制策略的研究，请参考文献10.1155/2022/5503137。~~
- [x] ~~6. 你是否考虑了~~~~**随机因素对谣言传播的影响**~~~~？~~
 
Thank you for your insightful comment. This paper primarily focuses on the role of opinion leaders in the spread of public opinion on social networks and does not delve into the specific impact of random factors on rumor dissemination. Although randomness in networks (such as unexpected events or individual spontaneous behavior) can significantly affect rumor propagation, this study is centered on how opinion leaders can guide public opinion for effective control, and thus does not include these random variables in the model. Future research could consider incorporating random factors along with network topology and the influence of opinion leaders to provide a more comprehensive understanding of the multifaceted aspects of rumor spread.
 
#### Reference
~~[1] Qiao, R., Hu, Y. Dynamic analysis of a SI1I2ADSI1I2AD information dissemination model considering the word of mouth. Nonlinear Dyn 111, 22763–22780 (2023). https://doi.org/10.1007/s11071-023-09021-5~~
~~[2] Pan, Wenqi, Yan, Weijun, Hu, Yuhan, He, Ruimiao, Wu, Libing, Dynamic Analysis and Optimal Control of Rumor Propagation Model with Reporting Effect, Advances in Mathematical Physics, 2022, 5503137, 14 pages, 2022. https://doi.org/10.1155/2022/5503137~~
 
### Rev.4
 
Rejectd
 
#### Comment
- [x] 1. 网络模型的构建和解释可以简化或进一步明确，以提高可读性。**建议使用更多的可视化图表或流程图来更清晰地展示建模过程。**具体来说，算法1中表达的内容没有以代码形式进行描述，而算法2的内容是公认的形式。在图3中，作者将KOL指标体系模型与信息转发模型的流程图合并。然而，整个过程的表示还不够直观和清晰。
 
1) 我已经重新修改了图例，增加了一些描述信息。同时，我在文中补充了用于描述图1的文字。
 
2) 我修改了算法1，让算法一更加清晰。
 
3) 我已经修改了图3，在图三中标注了对应的字母，希望这些修改可以更清晰直观。
 
- [x] ~~**2. 在表3中，参数的给出缺乏明确和可靠的过程。**~~~~例如，所谓的真实数据指的是什么？它是否是表4中提到的数据？~~~~**进行蒙特卡洛模拟的环境是什么？**~~~~该模型可能受益于进一步探讨分配给KOL影响力和活动的权重。或许可以讨论不同的权重或场景，以提供其影响的更全面视角。总的来说，这些权重的确定对模型至关重要。~~
 
1）抱歉，由于组织结构不清晰，导致您的疑惑。现在已经修改了表 3，将表3拆分成了表 3 和表 4 .现在表 3 已经被修正到正确的位置。表 3 中，参数由德尔菲法确定。表4中，部分参数由蒙特卡洛模拟确定。
 
2）对于德尔菲法。
 
3）真实数据指的是表 4 提到的数据。表 4 提供了对于真实数据集的部分描述，由于篇幅有限，无法将整个数据集完整描述在文中。因此，我将部分数据集放到了 github 上。
 
4）对于蒙特卡洛模拟，本研究使用 Python 语言进行 Monte Carlo 模拟，通过多线程在单机中并行计算。根据参数的不同设定，模拟次数为100-1000次不等，使用`concurrent.futures`库进行任务分配，以加速计算过程。
 
Thank you for your detailed feedback. We apologize for the initial lack of clarity in the organization, which may have contributed to confusion. We have made the following revisions to address these points:
 
+ We have restructured Table 3 by dividing it into two tables, now labeled as Table 3 and Table 4. Table 3 includes parameters determined through the Delphi method and has been moved to its appropriate location in the manuscript. Table 4 now contains parameters obtained via Monte Carlo simulations.
+ The term “real data” refers specifically to the dataset described in Table 4. Due to space limitations, we could not provide a complete description of the dataset within the manuscript. As such, a portion of the dataset has been made available on GitHub for reference.
+ For the Monte Carlo simulations, we used Python to conduct simulations on a single machine, utilizing multithreading to expedite the process. The number of simulation iterations varied between 100 and 1000, depending on specific parameter configurations. We used the `concurrent.futures` library for efficient task distribution, improving computational efficiency.
 
- [x] **3. 讨论部分可以扩展，以解决政府或组织如何在实际中实施控制策略，以及与操纵舆论相关的伦理问题。**
- [x] ~~**4. 结论部分可以更好地强调未来的研究方向**~~~~，特别是社交媒体平台的动态变化以及意见领袖角色的演变。~~
 
Thank you for your valuable feedback. We have revised the conclusion section to emphasize future research directions, particularly focusing on the dynamic changes in social media platforms and the evolving roles of opinion leaders. We appreciate your suggestion, which has helped improve the clarity and depth of our study’s implications.
 
This paper delves into the significant impact of opinion leader nodes on information spread in the field of network information security and public opinion control, proposing a set of specific control strategies based on these findings. It lays a solid foundation for future exploration in this research area.
 
While this study primarily focuses on the role of opinion leaders and dynamic network structures, future research could examine additional factors that influence the spread of online public opinion, such as content appeal, user interaction behaviors, and the potential impact of random factors, including unexpected events and spontaneous user reactions, on rumor propagation. These factors may alter the spread patterns significantly and highlight the need for adaptive strategies.
 
Furthermore, future research should consider the dynamic evolution of social media platforms and the evolving roles of opinion leaders as they adapt to new media formats and interactions. Expanding the scope of topics studied would also help validate the universality and adaptability of the proposed model and intervention strategies across diverse contexts. Other potential model enhancements could involve introducing variables such as personalized user characteristics, emotional polarity of topics, diversity of media, richness of content, and the time-varying characteristics of network structures. These extensions would increase the model's relevance to a wider range of public opinion contexts and deepen our understanding of complex information dissemination dynamics.
 
- [x] ~~5. 尽管该研究使用了模拟方法，但结合多个平台的现实案例研究（不仅限于新浪微博）将~~~~**增强文章的适用性。**~~
 
Thank you for this insightful suggestion.  We agree that incorporating real-world case studies across multiple platforms would enhance the applicability of our findings.  We have already included this point in the conclusion to highlight it as a direction for future research.  In future work, we plan to apply our models to a broader range of social media platforms beyond Sina Weibo to validate their effectiveness in different contexts.  This approach will help ensure that the model’s insights are generalizable across diverse public opinion environments.
 
Furthermore, future research should consider the dynamic evolution of social media platforms and the evolving roles of opinion leaders as they adapt to new media formats and interactions. Expanding the scope of topics studied would also help validate the universality and adaptability of the proposed model and intervention strategies across diverse contexts. Other potential model enhancements could involve introducing variables such as personalized user characteristics, emotional polarity of topics, diversity of media, richness of content, and the time-varying characteristics of network structures. These extensions would increase the model's relevance to a wider range of public opinion contexts and deepen our understanding of complex information dissemination dynamics.
 
- [ ] **6. 语言方面也需要彻底润色**，建议作者邀请英语母语者进行帮助。
- [x] ~~**7. 表1在正文中没有被引用**~~~~。此外，~~~~**表II-A多次被提及，但文本中并没有此表，只有表2。**~~
 
### Rev.5
 
Prepare A Major Revision
 
#### Comment
- [x] ~~1. 虽然该论文旨在突出其独特的贡献，但似乎回避了讨论已有文献中关于KOL（关键意见领袖）或社交网络结构在舆论治理和传播机制中的作用的研究。至关重要的是，承认并与这些现有研究进行对话，才能更好地确立当前研究的新颖性和进步。~~~~**现有的文献综述未能为所解决的研究空白提供有力的论据。**~~
 
Thank you for your valuable feedback. I have thoroughly revised the introduction to ensure a more comprehensive engagement with existing literature on the role of KOLs and social network structures in public opinion governance.
 
- [x] ~~2. 表1中呈现的比率的来源及具体计算未作充分说明。例如，~~~~**为什么“好友中心 0.5 ≤ 比率 ≤ 1.25”？**~~
 
Thank you for your question. The ratio range "FriendHub\ 0.5\le\mathrm{ratio}\le1.25" in Table 1 is based on findings from previous studies. We have now cited these sources in the manuscript to clarify the origin of this ratio and ensure the calculations are well-supported by existing research.
 
The Followee–Follower Ratio considers the quantitative re- lationship between a user’s followers and followees, measuring the extent to which a user follows others relative to how much they are followed in the social network.
 
- If the ratio approaches infinity, it indicates that the user might be a bot or an advertiser [34], such as an Information Seeker in Table I.
 
- If the ratio is close to 1, it means the number of followers and followees is similar, representing the most common type of reciprocity, such as Friends and Friend Hubs in Table I.
 
- If the ratio approaches zero, it suggests a stronger tendency towards content sharing and opinion expression, with the user focusing more on creating their content rather than following others, such as Information Sources in Table I.
 
Based on these criteria, we categorize users into four types: Information Source, Friend, Friend Hub, and Information Seeker [33], [35].
 
- [x] ~~**3. 存在格式不一致的问题，**~~~~特别是错误的引号和未解释的符号，如“表II-A”。此外，还存在多余的字符或词语，例如“X”： “基于这两个方面以及微博信息传播行为的特点，我们建立了一个意见领袖指标体系，详见下文。X” 建议进行彻底的校对，确保所有技术细节准确且无歧义地呈现。~~
- [x] ~~4. 仅使用“彩礼”~~~~**话题限制了关于舆论传播的结论的普适性**~~~~。未来的研究可以考虑更广泛的话题，以验证所提出的模型和最佳干预期的普遍性。~~
 
Thank you for your feedback.  We acknowledge that focusing exclusively on the “bride price” topic may limit the generalizability of our conclusions regarding public opinion propagation.  Based on your suggestion, we have revised the conclusion to reflect this consideration.  In future work, we plan to apply the proposed models and optimal intervention period to a broader range of topics to validate their universality and adaptability across different contexts.  This approach will help ensure that the model’s insights are applicable to a wider array of public opinion issues.
 
- [x] ~~5. 关于德尔菲法的应用：使用德尔菲法确定权重是值得称赞的，但~~~~**缺乏关于具体过程和最终权重的详细说明是一个明显的遗漏**~~~~。包含德尔菲程序的详细描述以及最终权重分配，将增强研究的可信性和可重复性。~~
 
Thank you for your valuable suggestion. We have revised the manuscript to include a detailed description of the Delphi method process used to determine the weights \omega_i, i \in \{1, 2, 3, \dots, 6\}. Specifically, we have clarified the selection criteria for experts and the multi-step process involved, including an open-ended survey, quantitative evaluation, and consensus refinement rounds. This iterative process ensured that expert opinions and the relative importance of each indicator were fully considered, resulting in a scientifically grounded evaluation system. Additionally, we have included the final parameter values in Table III for reference.
 
Due to the incommensurability of various indicators, this paper determines the weights ωi, i ∈ {1, 2, 3, . . .  , 6} using the Delphi method and conducts one-on-one interviews with experts (generally not exceeding 20).  The selected experts need to meet the following criteria: (i) expertise in public opinion control, (ii) availability, and (iii) willingness to par- ticipate in the Delphi panel [44].  The process included the following steps: 1) Open-ended Survey.  This round aimed to collect a broad range of views and establish a foundational understanding of expert opinions.  2) Quantitative Evaluation.  Based on feedback from Round 1, a structured questionnaire was designed, allowing experts to assign numerical weights to each indicator.  3) Consensus Refinement.  In this final round, experts were presented with the aggregated results from Round 2 and were encouraged to adjust their weights in light of the group’s feedback.  This iterative feedback loop continued until a consensus was reached on the weight values.  The opinions of the experts and the relative importance of the indicators are taken into account to ensure a scientific and reasonable evaluation system [45].  The parameters are shown in Table III.
 
总而言之，本文在舆论动态和干预策略领域有潜在的宝贵贡献。通过扩展文献综述、澄清数据和方法以及改进格式和研究结果的普适性，能够显著提高论文的质量和影响力。
 
#### Reference
~~[1] Huang, L. (2024). Risk assessment and governance path of social media rumors based on GRA and FsQCA. International Journal of Management Science and Engineering Management, 19(2), 167–175. https://doi.org/10.1080/17509653.2023.2253187~~
~~[2] Zongmin Li, Ye Zhao, Tie Duan, Jingqi Dai*. Configurational patterns for COVID-19 related social media rumor refutation effectiveness enhancement based on machine learning and fsQCA. Information Processing & Management 60 (2023) 103303.~~
 
### Rev.6
 
Accept With Minor Changes
 
#### Comment
- [x] ~~1. 应在摘要部分~~~~**添加一些关于社交网络舆论研究的经典论文**~~~~，以进一步丰富现有的研究。~~
- [x] ~~2. 简要~~~~**解释每个方程的意义**~~~~，特别是方程(6)和方程(10)的意义。此外，方程(15)和方程(16)是什么意思？~~
 
Thank you for your detailed feedback. Below is an explanation of the significance and meaning of each of the key equations mentioned:
 
1) Equation 6（现在是公式7）: 公式6基于 the influence of individual 和 the activity level of individual 定义了 the individual forwarding rate。它包含一个balancing coefficient to weigh the relative importance of activity and influence in calculating how actively an individual node (or person) is likely to spread information. Here, \( I_i \) and \( A_i \) represent the influence and activity of individual \( i \), while \( I_{max} \) and \( A_{max} \) are the maximum influence and activity in the network. This equation aims to quantify an individual's propensity to forward information based on their influence and activity level. 我们在文中对应的部分添加了相应的内容。
 
Accordingly, To more accurately describe the role of individuals in information spread and to quantify an individual’s tendency to forward information based on their influence and activity level. The individual forwarding rate is defined as the weighted sum of individual activity and individual influence:
 
2) Equation 10（现在是公式12）: 公式10，是公式9（现在是公式11）和公式7（现在是公式9）的延伸。公式7 is the **Logistic growth model for information spread** in the network, which describes how the proportion of infected (informed or influenced) nodes evolves over time. The growth rate is influenced by the **public opinion guidance factor** \( \eta(t) \) and the **individual forwarding rate** \( R_k \). Essentially, this equation models the spread of information over time, showing that as \( \eta(t) \) or \( R_k \) increase, information diffusion accelerates, increasing the proportion of influenced nodes in the network. 我们在文中公式9的位置添加了相应的补充。
 
Thus, the Logistic growth equation for the information forwarding model in the spread process can be expressed as follows, describing the evolution of the proportion of nodes forwarding information over time:
 
3) Equation 15、16（现在是公式17、18）:
 
The explanations for Equations 15 and 16 have also been revised in the manuscript.
 
By multiplying the spread efficiency and costeffectiveness as defined in Eq.15 and Eq.16, a comprehensive measure of information spread efficiency and cost-effectiveness at a given time τ is obtained. This measure is used to evaluate the effectiveness of information spread over time and the cost- effectiveness of intervention measures. It highlights the trade- off between maximizing information spread and minimizing intervention costs. Here, spread efficiency assesses the ca- pacity of information to spread through the network, while the cost-effectiveness of public opinion control indicates that early intervention and continuous monitoring of public opinion can effectively reduce the high costs of late-stage intervention. This metric simultaneously accounts for the dynamic nature of both information spread efficiency and public opinion control cost-effectiveness over time.
 
- [x] ~~3. 作者将提出的模型与现有模型进行了比较，但也应更详细地探讨KOL指标体系模型的创新设置所带来的贡献。因此，应该更好地讨论该模型带来的附加价值。~~
- [x] 4. 在给出政策建议的部分，尝试进一步结合数据和控制策略模型，使其更具说服力。
 
#### Reference
~~[1] Hassani, H., Razavi-Far, R., Saif, M., Chiclana, F., Krejcar, O., & Herrera-Viedma, E. (2022). Classical dynamic consensus and opinion dynamics models: A survey of recent trends and methodologies. Information Fusion, 88, 22-40.
~~~~[2] Morente-Molinera, J. A., Kou, G., Samuylov, K., Ureña, R., & Herrera-Viedma, E. (2019). Carrying out consensual group decision making processes under social networks using sentiment analysis over comparative expressions. Knowledge-Based Systems, 165, 335-345.~~
 
### Rev.7
 
Prepare A Major Revision
 
#### Comment
1. 作者应重写稿件以提高可读性、清晰度和严谨性。
- [x] ~~2. 论文缺乏对相关工作的详细讨论，导致边际贡献不明确且模糊。我建议~~~~**增加一个专门的文献综述部分。**~~~~此外，介绍中提到的研究空白是从意见领袖的角度缺乏公共舆论控制的考虑。然而，据我所知，已有大量相关文献存在。~~~~**作者需要进一步阐明研究空白/问题，并更有效地总结其贡献。**~~
- [x] ~~3. 本文内容组织不当；例如，“由于各指标间的不相容性，本文确定权重……”这段内容更适合放在“第III节 仿真与分析”中。文中有类似情况，~~~~**组织不当的内容影响可读性和理解**~~~~。我建议作者仔细审查稿件，更好地组织布局。~~
 
We appreciate your feedback regarding the organization of the manuscript. We have revised this section and moved the discussion on the weight parameters of the KOL indicator system model to Section 2.2, as shown in Table 3. We believe this change enhances the clarity and readability of the paper.
 
- [x] ~~4. 本文多次提到表II-A，包括在第2页和第3页，但在文中找不到此表。例如，在第2页提到：“如果比率接近无穷大，表示该用户可能是机器人或广告商[30]，如表II-A中的信息寻求者。”在第3页提到：“图2显示了基于跟随者和被关注者关系演变的集群社交网络模型演变结束时的网络结构，网络规模详~~~~**见表II-A。”**~~
 
Thank you for your valuable feedback regarding the references to Table I. I apologize for the oversight that caused Table I to be incorrectly rendered as Table II-A during the LaTeX rendering process. I have now corrected this issue, and Table I is properly formatted and positioned within the manuscript. Thank you for your understanding.
 
- [x] ~~5. 在算法2“意见领袖节点识别”的第4步中，表述为“4：node_score ← compute_score(𝑛𝑜𝑑𝑒.𝐼𝑖, 𝑛𝑜𝑑𝑒.𝐴𝑖)”。排序是如何完成的？手稿未明~~~~**确说明compute_score(𝑛𝑜𝑑𝑒.𝐼𝑖, 𝑛𝑜𝑑𝑒.𝐴𝑖)的确切计**~~~~算方法。~~
 
感谢您对我们工作的细致审查以及提出的宝贵意见。我们已经认真考虑了您的建议，并对算法2中的“意见领袖节点识别”过程进行了进一步的阐述和澄清。以下是对您提出问题的回复：
 
在算法2的第4步中，我们确实没有详细说明`compute_score(node.Ii, node.Ai)`的计算方法。为了提高算法的透明度和可理解性，我们已经在算法的伪代码中添加了相应的注释，并对`compute_score`函数进行了详细说明。
 
具体来说，`compute_score`函数的目的是综合考虑节点的影响力（`node.Ii`）和活跃度（`node.Ai`）来计算其得分。这一得分将作为后续排序的依据。以下是`compute_score`函数的计算方法：
 
在算法2中，我们使用这个函数来计算每个节点的得分，然后根据得分对节点进行排序。以下是更新后的算法2的伪代码：
 
在第4步中，我们为每个节点计算得分，并将其存储在`node.scores`中。在第7步中，我们根据`node.scores`对所有节点进行降序排序。这样，得分最高的节点将排在前面，从而被识别为意见领袖节点。
 
我们希望这些更新能够清楚地说明排序的完成方式以及`compute_score(node.Ii, node.Ai)`的确切计算方法。我们相信这些修改将使算法更加清晰易懂，并有助于读者更好地理解和复现我们的研究。
 
- [x] ~~6. 在第5页，声明“结合Eq. 4和5，信息转发模型在传播过程中的Logistic增长方程可以表示为”，但“Eq. 4和5”~~~~**实际上应为“Eq. 5和6”**~~~~。此外，方程（10）的表达似乎不正确，~~~~**乘法符号后的表达应在指数𝑒的上标中。**~~
 
Thank you for your suggestion. I have corrected the reference to the equations on page 5, changing “Eq. 4 and 5” to “Eq. 5 and 6.” Additionally, I have revised Equation (10) to ensure clarity in the expression of the exponent. The length of the exponent was causing confusion, so I have shortened the equation for better readability. Thank you for your understanding, and I appreciate your feedback!
 
- [x] ~~7. 建议在图中的x和y轴添加描述性文本，而不仅仅是使用严格的数学符号，~~~~**例如图4、图6(b)和图8。此外，图8中的子图(a)未标记字母"a"。**~~
 
Thank you for your valuable feedback. We have added descriptive text to the x and y axes in Figures 4 and 6(b) to enhance readability as suggested. Additionally, we have labeled subplot (a) in Figure 8 with the letter "a".
 
- [x] ~~**8. 手稿中有许多标点符号缺失的情况**~~~~。例如，第9页的句子“控制策略模型的示意图如图9所示，最后通过综合考虑这两个因素提供结论和政策指导建议。”~~~~**应在“图9”和“最后”之间加上句号。**~~~~文中还有类似的问题，请仔细检查。~~
- [x] ~~9. 作者可能误解了“富俱乐部”效应的含义。在第8页，~~~~**“富俱乐部”效应的解释为“在高顶点度范围内，真实社交网络在顶点度增加时平均邻居度略有下降，这一现象在社交网络分析中称为‘富俱乐部’效应，高度连接的顶点往往与较小度的顶点相连。”然而，富俱乐部效应实际上是指高度连接的顶点倾向于优先连接其他高度连接的顶点。**~~
- [x] ~~10. 能否请作者澄清为何~~~~**方程14中的分母设置为100，如果使用其他值会得到什么结果？**~~
 
 Thank you for your question regarding the denominator value of 100 in Equation (14).
 
分母设置为100是根据特定的参数要求而选择的。在整个传播过程中，即使在 free propagation 情况下到达稳态<img src="/master/img/b0fc9aac91383a31aee15eb63345eee4.svg" alt="image" />最大传播轮次也仅需要1250。而在有意见领袖参与的情况下，仅需要600轮次即可到达稳态<img src="/master/img/b0fc9aac91383a31aee15eb63345eee4.svg" alt="image" />。在公式14中<img src="/master/img/0e852ba0acfeec16fc062910ab4a54e4.svg" alt="image" />，分母为100是因为我们讨论的都是有意见领袖参与情况下的控制成本，而<img src="/master/img/38580b59074e198001fae5ac0e45d53c.svg" alt="image" />，这里还留出了400冗余，保证了灵活性和可扩展性。
 
**附一个图这里**
 
- [x] ~~11. 在第9页，表述“在不考虑正或负干预的情况下，~~~~**最优干预期为15% ≤ τ ≤ 32%”引发了一个问题：这一结论是如何得出的？**~~~~我在图10中~~~~**没有看到“在不考虑正或负干预”的曲线。**~~~~此外，第8页提到，“这两种干预方法对应于模型中不同的参数设置和机制，以模拟现实中的不同传播环境和干预方法”~~~~**，但文中并未详细说明参数的具体差异。**~~
 
感谢审稿人的宝贵意见。
 
1.关于不区分干预方向的最佳介入区间：我们确实没有在图10中专门绘制“无正向或负向干预的”曲线，因为这个结果是通过对比正向和负向干预的趋势曲线而得出的。具体过程是：在0-100%区间内，间隔1%做干预，得到正向和负向干预下的最佳成本峰值点分别为正向干预：15%，反向干预：32%。因此，我们在此基础上得出结论，即在不考虑干预方向的情况下，15% ≤ τ ≤ 32%是最优的干预区间。
 
2. 关于不同干预方式的参数设置差异：正向和负向干预的模型设置不同，是为了模拟不同的传播环境和干预方式。在具体参数上，正向干预主要通过增加传播概率来实现，而负向干预则通过降低传播概率来模拟。我们在文中修改了这一可能导致文章不清晰的部分。
 
The public opinion guidance factor is divided into positive guidance and negative guidance. Positive guidance refers to behavior in which opinion leaders align with mainstream opinions and further amplify information spread, thereby promoting broader dissemination. The purpose of positive guidance is to incrementally strengthen the influence of public opinion, as shown in Eq.5.
 
where \eta\left(0\right) is the initial opinion guidance factor, N_o\left(t\right) is the number of opinion leader nodes at time t，V_I\left(t\right) is the number of I-state nodes in the network at time t, and \omega_P is the public opinion coefficient, reflecting the extent to which public opinion guidance affects the information spread rate.
 
In contrast, negative guidance involves opinion leaders deliberately spreading information that contradicts mainstream opinions, aiming to influence the path and reach of information spread by generating controversy or encouraging counter-dissemination. The purpose of negative guidance is to gradually attenuate and weaken the impact of public opinion, as shown in Eq.6.
 
- [x] ~~12. 最后，由于仿真结果是通过蒙特卡洛仿真获得的，~~~~**论文应具体说明实验重复多少次以获得这些结果。**~~
 
### Rev.8
 
Reject
 
#### Comment
- [x] ~~1. KOL（关键意见领袖）在摘要中未解释清楚。~~
- [x] ~~2. 在引言的开头有两个“in”。~~
 
Thank you for pointing out the repetition of "in" at the beginning of the introduction. I have made the necessary revisions to eliminate this redundancy and improve the clarity of the text. I appreciate your careful review!
 
- [x] ~~3. 引言中引用了许多文献，但我认为这些文献中没有涉及舆论动态或社交网络领域的重要工作。~~
- [x] ~~4. 在第一页的右侧部分，出现了“a.”和“b.”，这是什么意思？在“a.”之前，文章并没有提到“现有工作有以下两个主要限制（或类似表述）...”。~~
 
Thank you for pointing this out. I have revised the introduction to clarify the structure, replacing "a." and "b." with "1)" and "2)" to avoid any ambiguity. This change should improve readability and ensure that the limitations are clearly presented. I appreciate your attention to detail!
 
- [x] ~~5. 表1在正文中没有提及。~~
- [x] ~~6. 在第2页，“构建步骤如算法II-A所示：”，但是算法II-A在哪里？~~
- [x] 7. 在算法1的步骤3中，(i,j)∈1,2,...,N_T。∈表示“属于”，后面应该是一个集合，但1,2,...,N_T并不是一个集合。此外，(i,j)是一个对，如何属于一个集合？最后，在步骤3中，G_T=(V_T, E_T)，但是E_V_i,V_j，如何理解这一点？E_T下只有T，但在E_V_i,V_j下有V_i和V_j，这是什么意思？也就是说，E_0表示0的节点集，但E_1,2，是什么意思？
- [x] ~~8. KOL在第II节的B部分中首次出现。然而，它应该在第一次出现时就给出定义。~~
- [x] ~~9. 引用格式需要改进。例如，“Gu et al.......[34]”应该写作“Gu et al.[34]......”。类似错误很多。~~
- [x] ~~10. 在方程(2)中，I_i是什么意思？在方程右侧没有“i”这个变量，如何得到I_i？方程(3)中也是如此。~~
 
Thank you for highlighting this point. In Equation (2), IiI_iIi represents the influence of individual iii within the model, and is derived from parameters on the right side of the equation. To clarify, I have now revised the text to specify that IiI_iIi denotes the influence attributed to individual iii, making its role and origin in the model clearer. Additionally, I made similar adjustments in Equation (3) to ensure consistent and unambiguous use of iii throughout.
 
- [x] ~~11. i∈(1,2,3,...6)，这对吗？∈后面应该是一个集合，但(1,2,3,...6)是一个向量。~~
 
Thank you for your valuable feedback. In the original draft, we used i∈(1,2,3,…,6)i \in (1,2,3,\ldots,6)i∈(1,2,3,…,6), which could indeed lead to confusion as it implies a vector rather than a set. We have revised this to i∈{1,2,3,…,6}i \in \{1,2,3,\ldots,6\}i∈{1,2,3,…,6}, to more accurately indicate that iii belongs to this set. Thank you again for helping us clarify this point.
 
- [x] 12. 在方程(5)中，V_I表示I阶段的节点，I是一个变量，但是w_P是舆论系数，这里P似乎不是一个变量，但它与V_I形式相同，令人困惑。
 
在这里，I不是一个变量，I表示状态为I的节点数量。V_I(t) 表示t时刻网络中状态为I的节点数量。
 
\omega_P，\omega_R 均表示为常量。
 
在文中，带有角标的I，如I_i，其中，I表示个体影响力，i表示个体。
 
不在角标位置的i，代表转发信息的个体数量占总个体的比例。
 
为了避免I所带来的歧义，在后续公式7,8,9,10,11中，全部使用di/dt代替了dI/dt。
 
- [x] ~~13. 在方程(6)中，这个方程正确吗？还是应该是(1-w_R)，括号是否遗漏了？在方程(6)下方，文中说“I_i表示个人i的影响力”，I_i与方程(3)中的I_i相同吗？但在方程(3)中，右侧没有“i”。~~
 
在方程6中，I_i表示个人i的影响力，和方程3中的I_i相同。A_i表示个体活跃度，和方程4中的A_i相同。
 
- [x] ~~14. 在方程(7)下方，I(t)是节点的数量，但在方程(7)中，没有I(t)，只有V_I(t)，似乎I是V的下标，而(t)与V相同。此外，这里还使用了I，而在上面用的是I_i，但它们的含义不同。~~
 
Thank you for identifying this issue. There was an error in Equation (7), where V_I(t) was incorrectly written as V_{I(t)}. We have corrected this to ensure consistency. Here, V_I(t) represents the number of nodes in the I-state at time t. We appreciate your attention to this detail.
 
- [x] ~~15. 在方程(7)中，最后一部分“is”是什么意思？方程(7)下方没有解释。~~
 
Thank you for your observation regarding Eq. (7). We have added a corresponding explanation below the equation to clarify the meaning of the term "is." This addition provides context and helps to ensure that readers understand the significance of the last part of the equation. We appreciate your feedback, which has contributed to improving the clarity of the paper.
 
- [x] ~~16. 在方程(9)中，左侧的i(t)是什么意思？因为在右侧部分，i(1-i)t，意思是“i”和“t”是数值，那么i(t)是什么？~~
 
这里犯了一个错误，已经更正方程9。
 
Thank you for pointing this out. The error in the equation was due to an oversight, and we have now corrected it. We appreciate your careful review.
 
- [x] ~~17. 在方程(10)中，为什么i_0 = 0.007？~~
 
Thank you for your question. In Equation (10), the initial value i= 0.007 was selected based on empirical data and serves as the baseline proportion of individuals initially influenced or “infected” within the network. This value reflects the small initial seed group typically observed in real-world information spread scenarios, which allows for realistic simulation of the propagation process from a limited starting point.
 
- [x] ~~18. 在表3中，参数为什么设置为这些值？是否有任何规则？~~
- [x] 19. 在方程(13)中，E(τ)表示传播效率，但是上文中E已经表示为边了
 
Thank you for pointing this out. In the manuscript, \( E \) is indeed used in two distinct contexts: first as the edge set in the network model, and later as the spread efficiency in Equation (13). These two uses of \( E \) are context-dependent and are clarified by their surrounding notation and context.
 
To avoid any potential confusion, we have reviewed the manuscript to ensure that each use of \( E \) is defined clearly in its respective context. In particular, references to \( E \) as the edge set are always associated with node pairs or edge relationships (e.g., \( E_{v_i, v_j} \)), while \( E(\tau) \) denotes spread efficiency within the specific context of Equation (13).
 
### Rev.9
 
Accept With Minor Changes
 
#### Comment
- [x] ~~1. 论文提到意见控制策略，但这些策略应在论文早期的贡献部分具体描述。~~
- [ ] 2. 图2提供了一个具体示例，这值得称赞；然而，标明一些与网络构建方法改进相关的主要属性将更有益。
- [x] ~~3. 在算法2的第7行中，num top nodes ← ⌈α × length(sorted nodes)/100⌉表明α可能代表百分比σ。~~
- [x] ~~4. 目前不清楚方程8的具体位置在哪里。~~
 
Thank you for your comment. Equation 8 (now Equation 10) has been moved to a more prominent position near the top of the section for improved visibility and clarity.
 
- [x] ~~5. 尽管方程12的结果已得到验证，但能否对i0 = 0.007的设置进行解释？~~
- [x] ~~6. 表2中的参数提到使用德尔菲法，但这些参数在表3中也出现，并引用了蒙特卡罗方法进行参数设置，可能导致混淆。~~
- [x] ~~7. 我建议进一步详细描述表4中使用的真实数据集的基本特征，以增强整体数据展示的可信度。~~
 
将数据集进行开源
 
- [x] ~~8. 方程14中提出的成本增长函数应进一步明确其设置背后的理论依据。~~
 
Thank you for your suggestion. The rationale behind the cost growth function in Equation 14 is that early intervention is significantly more cost-effective compared to delayed intervention in public opinion control. We have revised the manuscript to clarify this point and enhance readability.
 
To maintain social stability and public order, regulatory authorities often implement various interventions in response to public opinion spread [51], [52]. These measures incur both direct and indirect costs, which tend to escalate significantly with time. Timely interventions during the initial stages of spread are relatively low-cost and can effectively control pub- lic opinion, while delayed interventions face rapidly increasing costs due to the accelerated spread and entrenchment of public opinion.
 
Therefore, the cost-effectiveness of intervention is modeled as an exponentially growing function over time, given by:
 
- [x] ~~9. 有一点令人困惑的是，虽然前面的部分提出了时间变化的动态网络构建过程，但在第4节讨论的控制策略中，是否考虑了网络的动态演化？~~
 
在第四节中，所有的结果均是基于第三节中的仿真结果。
 
### Rev.10
 
Accept With Minor Changes
 
#### Comment
- [x] 1. 该研究很有趣，然而，需要对文本进行深入审查，以达到更高质量和清晰度的文章，使读者和研究者更容易理解。
- [x] 2. 请在论文中添加所提控制策略的完整框架。
 
Thank you for your suggestion.  The complete framework of the proposed control strategy is presented in Figure 3.  Additionally, Figure 3 has been revised to include symbols corresponding to the equations used in this paper.  We hope these adjustments provide greater clarity in understanding the control strategy presented.
 
- [x] 3. 仿真结果已被分析和验证。请提供一些基线策略（baseline strategies）以进行比较，并简要描述这些基线策略。

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