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Opinion Maximization in Social Networks by Modifying Internal Opinions

Gengyu Wang, Runze Zhang, Zhongzhi Zhang

TL;DR

This work tackles maximizing the overall expressed opinion in social networks by selectively fixing the internal opinions of $k$ nodes. It introduces two sampling-based methods and a deterministic asynchronous exact-selection algorithm, leveraging absorbing random walks and spanning-forest interpretations to estimate node influence and identify the optimal set with rigorous error guarantees. The proposed MIS framework demonstrates near-optimal accuracy and scalable performance on networks with tens of millions of nodes, outperforming standard baselines and exact-inversion approaches. The results suggest practical applicability to large-scale opinion governance, with potential extensions to dynamic and multi-opinion settings.

Abstract

Public opinion governance in social networks is critical for public health campaigns, political elections, and commercial marketing. In this paper, we addresse the problem of maximizing overall opinion in social networks by strategically modifying the internal opinions of key nodes. Traditional matrix inversion methods suffer from prohibitively high computational costs, prompting us to propose two efficient sampling-based algorithms. Furthermore, we develop a deterministic asynchronous algorithm that exactly identifies the optimal set of nodes through asynchronous update operations and progressive refinement, ensuring both efficiency and precision. Extensive experiments on real-world datasets demonstrate that our methods outperform baseline approaches. Notably, our asynchronous algorithm delivers exceptional efficiency and accuracy across all scenarios, even in networks with tens of millions of nodes.

Opinion Maximization in Social Networks by Modifying Internal Opinions

TL;DR

This work tackles maximizing the overall expressed opinion in social networks by selectively fixing the internal opinions of nodes. It introduces two sampling-based methods and a deterministic asynchronous exact-selection algorithm, leveraging absorbing random walks and spanning-forest interpretations to estimate node influence and identify the optimal set with rigorous error guarantees. The proposed MIS framework demonstrates near-optimal accuracy and scalable performance on networks with tens of millions of nodes, outperforming standard baselines and exact-inversion approaches. The results suggest practical applicability to large-scale opinion governance, with potential extensions to dynamic and multi-opinion settings.

Abstract

Public opinion governance in social networks is critical for public health campaigns, political elections, and commercial marketing. In this paper, we addresse the problem of maximizing overall opinion in social networks by strategically modifying the internal opinions of key nodes. Traditional matrix inversion methods suffer from prohibitively high computational costs, prompting us to propose two efficient sampling-based algorithms. Furthermore, we develop a deterministic asynchronous algorithm that exactly identifies the optimal set of nodes through asynchronous update operations and progressive refinement, ensuring both efficiency and precision. Extensive experiments on real-world datasets demonstrate that our methods outperform baseline approaches. Notably, our asynchronous algorithm delivers exceptional efficiency and accuracy across all scenarios, even in networks with tens of millions of nodes.
Paper Structure (29 sections, 15 theorems, 40 equations, 7 figures, 3 tables, 5 algorithms)

This paper contains 29 sections, 15 theorems, 40 equations, 7 figures, 3 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Problem Formulation
  5. Sampling Methods
  6. Fast Exact-Selection Method via Asynchronous Updates
  7. Asynchronous Update-Based Approximation
  8. Fast Exact-Selection Algorithm
  9. Experiments
  10. Limitations
  11. Conclusion
  12. Omitted Proofs
  13. Proof of Lemma \ref{['lem:1']}
  14. Proof of Lemma \ref{['lem:2']}
  15. Proof of Theorem \ref{['the:1']}
  16. ...and 14 more sections

Key Result

Lemma 1

For an unweighted graph $\mathcal{G}=(V,E)$, let $\boldsymbol{\mathit{p}}_i \in \mathbb{R}^{|V|}$ be the absorption probability vector of absorbing random walks starting at node $i \in V$. The structural centrality of node $v$ is $\rho_v = \sum_{i \in V} \boldsymbol{\mathit{p}}_i(v)$.

Figures (7)

  • Figure 1: Performance of algorithms in accuracy across four smaller graphs.
  • Figure 2: Performance of algorithms in accuracy across four larger graphs.
  • Figure 3: Running time of algorithm MIS under different resistance coefficient distributions.
  • Figure 4: Performance of algorithms in accuracy under normal distribution.
  • Figure 5: Performance of algorithms in accuracy under normal distribution.
  • ...and 2 more figures

Theorems & Definitions (16)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Corollary 1
  • Lemma 3
  • Theorem 2
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • Lemma 7
  • ...and 6 more