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A Novel Discrete-time Model of Information Diffusion on Social Networks Considering Users Behavior

Tran Van Khanh, Do Xuan Cho, Hoang Phi Dung

TL;DR

The paper extends the classical SIR model with a Delayable state to better capture user behavior in online diffusion, and derives a mean-field, discrete-time SDIR system. It proves a sufficient convergence condition based on spectral radius and formulates an edge-deletion problem to minimize diffusion, introducing tight supermodular upper and lower bounds and a Sandwich approximation framework. Two algorithms, greedy and sandwich-based, are proposed to approximate the NP-hard optimization, with theoretical guarantees and empirical validation on real networks showing enhanced diffusion control and faster convergence. Overall, the work provides a tractable approach to modeling nuanced user behavior in information spread and offering practical edge-deletion strategies for diffusion minimization.

Abstract

In this paper, we introduce the SDIR (Susceptible-Delayable-Infected-Recovered) model, an extension of the classical SIR epidemic framework, to provide a more explicit characterization of user behavior in online social networks. The newly merged state D (delayable) represents users who have received the information but delayed its spreading and may eventually choose not to share it at all. Based on the mean-field approximation method, we derive the dynamical equations of the model and investigate its convergence and stability conditions. Under these conditions, we further propose an approximation algorithm for the edge-deletion problem, aiming to minimize the influence of information diffusion by identifying approximate solutions.

A Novel Discrete-time Model of Information Diffusion on Social Networks Considering Users Behavior

TL;DR

The paper extends the classical SIR model with a Delayable state to better capture user behavior in online diffusion, and derives a mean-field, discrete-time SDIR system. It proves a sufficient convergence condition based on spectral radius and formulates an edge-deletion problem to minimize diffusion, introducing tight supermodular upper and lower bounds and a Sandwich approximation framework. Two algorithms, greedy and sandwich-based, are proposed to approximate the NP-hard optimization, with theoretical guarantees and empirical validation on real networks showing enhanced diffusion control and faster convergence. Overall, the work provides a tractable approach to modeling nuanced user behavior in information spread and offering practical edge-deletion strategies for diffusion minimization.

Abstract

In this paper, we introduce the SDIR (Susceptible-Delayable-Infected-Recovered) model, an extension of the classical SIR epidemic framework, to provide a more explicit characterization of user behavior in online social networks. The newly merged state D (delayable) represents users who have received the information but delayed its spreading and may eventually choose not to share it at all. Based on the mean-field approximation method, we derive the dynamical equations of the model and investigate its convergence and stability conditions. Under these conditions, we further propose an approximation algorithm for the edge-deletion problem, aiming to minimize the influence of information diffusion by identifying approximate solutions.
Paper Structure (15 sections, 8 theorems, 12 equations, 3 figures, 2 algorithms)

This paper contains 15 sections, 8 theorems, 12 equations, 3 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Proposed Model
  3. Sufficient Condition for Global Convergence
  4. The Problems and bounding functions
  5. The main problem
  6. Supermodular Upper Bound
  7. Supermodular Lower Bound
  8. Algorithms
  9. Experiments
  10. Comparison with Heuristic Algorithms
  11. Convergence Analysis
  12. Conclusion
  13. Proof of Theorem \ref{['convergence']}
  14. Proof of Theorem \ref{['upbound']}
  15. Proof of Theorem \ref{['lowbound']}

Key Result

Theorem 3.1

Under Assumption as1, there always exists a choice of vector $\bm{q}\in(0,1]^{n}$ such that $\rho(\bm{M})\leq\rho(\bm{M}_{\text{SIR}})$. Moreover, if $\rho(\bm{M})<1$ then $\bm{x}(t)$ and $\bm{y}(t)$ converge to the $\bm{0}_{n\times1}$.

Figures (3)

  • Figure 1: The SDIR model
  • Figure 2: Haslemere Network with preprocessing
  • Figure 3: Convergence of infection states over time

Theorems & Definitions (11)

  • Theorem 3.1
  • Corollary 3.2
  • Definition 4.1
  • Theorem 4.3
  • Lemma 4.4
  • Theorem 4.5
  • Lemma 4.6
  • Proposition 5.1
  • Remark 5.2
  • Lemma 7.1
  • ...and 1 more