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Supervised centrality via sparse network influence regression: an application to the 2021 Henan floods' social network

Yingying Ma, Wei Lan, Chenlei Leng, Ting Li, Hansheng Wang

TL;DR

The paper tackles the limitation of topology-only centrality by introducing supervised centrality via the sparse network influence regression (SNIR) model, which yields node-specific, sparse influence parameters $\rho_j$ in the network response equation $Y_i = \mu_i + \sum_j \rho_j a_{ij} Y_j + \varepsilon_i$. It develops a scalable estimation strategy based on conditional quasi-maximum likelihood and a forward-addition screening procedure with EBIC for model selection, establishing screening consistency and asymptotic normality on the selected set. Applied to the 2021 Henan Floods Sina Weibo data, SNIR identifies task-specific influential users for three response types (reposts, comments, likes) and shows improved fit over SAR while revealing influential actors not captured by purely topology- or response-based methods. Extensive simulations corroborate the method’s ability to recover true influencers in large, sparse networks and demonstrate computational efficiency, with potential extensions to dynamics and covariates. The work provides a robust, scalable framework for task-driven centrality that can guide information propagation and misinformation mitigation in large social networks.

Abstract

The social characteristics of players in a social network are closely associated with their network positions and relational importance. Identifying those influential players in a network is of great importance as it helps to understand how ties are formed, how information is propagated, and, in turn, can guide the dissemination of new information. Motivated by a Sina Weibo social network analysis of the 2021 Henan Floods, where response variables for each Sina Weibo user are available, we propose a new notion of supervised centrality that emphasizes the task-specific nature of a player's centrality. To estimate the supervised centrality and identify important players, we develop a novel sparse network influence regression by introducing individual heterogeneity for each user. To overcome the computational difficulties in fitting the model for large social networks, we further develop a forward-addition algorithm and show that it can consistently identify a superset of the influential Sina Weibo users. We apply our method to analyze three responses in the Henan Floods data: the number of comments, reposts, and likes, and obtain meaningful results. A further simulation study corroborates the developed method.

Supervised centrality via sparse network influence regression: an application to the 2021 Henan floods' social network

TL;DR

The paper tackles the limitation of topology-only centrality by introducing supervised centrality via the sparse network influence regression (SNIR) model, which yields node-specific, sparse influence parameters in the network response equation . It develops a scalable estimation strategy based on conditional quasi-maximum likelihood and a forward-addition screening procedure with EBIC for model selection, establishing screening consistency and asymptotic normality on the selected set. Applied to the 2021 Henan Floods Sina Weibo data, SNIR identifies task-specific influential users for three response types (reposts, comments, likes) and shows improved fit over SAR while revealing influential actors not captured by purely topology- or response-based methods. Extensive simulations corroborate the method’s ability to recover true influencers in large, sparse networks and demonstrate computational efficiency, with potential extensions to dynamics and covariates. The work provides a robust, scalable framework for task-driven centrality that can guide information propagation and misinformation mitigation in large social networks.

Abstract

The social characteristics of players in a social network are closely associated with their network positions and relational importance. Identifying those influential players in a network is of great importance as it helps to understand how ties are formed, how information is propagated, and, in turn, can guide the dissemination of new information. Motivated by a Sina Weibo social network analysis of the 2021 Henan Floods, where response variables for each Sina Weibo user are available, we propose a new notion of supervised centrality that emphasizes the task-specific nature of a player's centrality. To estimate the supervised centrality and identify important players, we develop a novel sparse network influence regression by introducing individual heterogeneity for each user. To overcome the computational difficulties in fitting the model for large social networks, we further develop a forward-addition algorithm and show that it can consistently identify a superset of the influential Sina Weibo users. We apply our method to analyze three responses in the Henan Floods data: the number of comments, reposts, and likes, and obtain meaningful results. A further simulation study corroborates the developed method.

Paper Structure

This paper contains 22 sections, 4 theorems, 60 equations, 5 figures, 12 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Henan Floods Social Network
  3. Sparse Network Influence Regression
  4. The Model
  5. General estimation approach
  6. Parameter estimation with unknown support
  7. Comparison of Algorithm 1 with other algorithms
  8. Real Data Analysis
  9. Simulation
  10. Synthetic data
  11. Simulation based on the real data
  12. Discussion
  13. Theoretical Conditions
  14. A Dynamic Model
  15. The choice of candidate set $\mathcal{M}$ in real data analysis
  16. ...and 7 more sections

Key Result

Theorem 3.1

Under Conditions (C1)--(C6) discussed in Appendix sec:condition, as $N \rightarrow \infty$, with probability tending to one, (1) the forward-addition algorithm finds a superset of $\mathcal{S}_1$ in $m^*$ steps. That is, $P( \mathcal{S}_1 \subset \mathcal{S}^{(m^*)}) \rightarrow 1$; (2) we have $P(

Figures (5)

  • Figure 1: The histogram of in-degrees (left) and out-degrees (right) for Henan Floods network.
  • Figure 2: Density plot of reposts, comments and likes after logarithm transformation.
  • Figure 3: A hypothetical network for SNIR model. The size of each user is proportional to its in-degree. Black users are influential and white users are non-influential.
  • Figure 4: Empirical distributions of the three responses.
  • Figure 5: Proportion of correctly detected influential users as the signal-to-noise ratio (SNR) increases for various response types.

Theorems & Definitions (5)

  • Remark 1
  • Theorem 3.1
  • Corollary 1
  • Theorem E.1
  • Theorem E.2