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Preserving Core Structures of Social Networks via Information Guided Multi-Step Graph Pruning

Yutong Hu, Bingxin Zhou, Jing Wang, Weishu Zhao, Liang Hong

TL;DR

The paper addresses preserving semantic backbone in dense graphs by framing graph semantics with mutual information, specifically tracking $I({\mathcal{G}};{\mathcal{G}}_k)$ and $I({\bm{Y}};{\mathcal{G}}_k)$. It introduces IGPrune, a differentiable, gradient-boosting-inspired multi-step pruning algorithm that progressively removes edges to maximize a lower bound on $I({\mathcal{G}};{\bm{Y}})$ while reducing edges. The framework provides local and global evaluation metrics, including a complexity score, information score, AUC-IC, and IBP, and demonstrates via extensive experiments that IGPrune preserves task-relevant information and reveals interpretable backbones. The empirical results on social and biological networks show improved information–complexity trade-offs and scalable performance relative to baselines, enabling scientific discovery through interpretable backbone extraction.

Abstract

Social networks often contain dense and overlapping connections that obscure their essential interaction patterns, making analysis and interpretation challenging. Identifying the structural backbone of such networks is crucial for understanding community organization, information flow, and functional relationships. This study introduces a multi-step network pruning framework that leverages principles from information theory to balance structural complexity and task-relevant information. The framework iteratively evaluates and removes edges from the graph based on their contribution to task-relevant mutual information, producing a trajectory of network simplification that preserves most of the inherent semantics. Motivated by gradient boosting, we propose IGPrune, which enables efficient, differentiable optimization to progressively uncover semantically meaningful connections. Extensive experiments on social and biological networks show that IGPrune retains critical structural and functional patterns. Beyond quantitative performance, the pruned networks reveal interpretable backbones, highlighting the method's potential to support scientific discovery and actionable insights in real-world networks.

Preserving Core Structures of Social Networks via Information Guided Multi-Step Graph Pruning

TL;DR

The paper addresses preserving semantic backbone in dense graphs by framing graph semantics with mutual information, specifically tracking and . It introduces IGPrune, a differentiable, gradient-boosting-inspired multi-step pruning algorithm that progressively removes edges to maximize a lower bound on while reducing edges. The framework provides local and global evaluation metrics, including a complexity score, information score, AUC-IC, and IBP, and demonstrates via extensive experiments that IGPrune preserves task-relevant information and reveals interpretable backbones. The empirical results on social and biological networks show improved information–complexity trade-offs and scalable performance relative to baselines, enabling scientific discovery through interpretable backbone extraction.

Abstract

Social networks often contain dense and overlapping connections that obscure their essential interaction patterns, making analysis and interpretation challenging. Identifying the structural backbone of such networks is crucial for understanding community organization, information flow, and functional relationships. This study introduces a multi-step network pruning framework that leverages principles from information theory to balance structural complexity and task-relevant information. The framework iteratively evaluates and removes edges from the graph based on their contribution to task-relevant mutual information, producing a trajectory of network simplification that preserves most of the inherent semantics. Motivated by gradient boosting, we propose IGPrune, which enables efficient, differentiable optimization to progressively uncover semantically meaningful connections. Extensive experiments on social and biological networks show that IGPrune retains critical structural and functional patterns. Beyond quantitative performance, the pruned networks reveal interpretable backbones, highlighting the method's potential to support scientific discovery and actionable insights in real-world networks.

Paper Structure

This paper contains 44 sections, 2 theorems, 16 equations, 6 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Graph Summarization
  4. Edge Sparsification
  5. Mutual Information in Deep Learning
  6. Problem Formulation: Graph Semantics as Mutual Information
  7. Problem Setup and Notations
  8. Multi-Step Graph Pruning
  9. Mutual Information for Graph Pruning
  10. Structural information preservation
  11. Task-relevant information
  12. Task-Based Mutual Information Estimation
  13. Evaluation Metrics: Local and Global Scoring
  14. Local Measurements
  15. Global Measurements
  16. ...and 29 more sections

Key Result

Proposition 1

Let $q_\phi({\bm{Y}}\mid{\mathcal{G}})$ be a parametric predictor with learnable parameters $\phi$, trained on labeled samples $\{({\mathcal{G}}_i, y_i)\}_{i=1}^M$ to approximate $p({\bm{Y}}\mid{\mathcal{G}})$. Then, the MI between the graph ${\mathcal{G}}$ and the task target ${\bm{Y}}$ can be lowe where $M$ denotes the number of labeled samples, $y_i$ is the task label of sample $i$, and $\hat{H

Figures (6)

  • Figure 1: Illustrative Figure. IGPrune iteratively prunes edges based on gradients guided by information $I(Y_1;{\mathcal{G}}_3)$, gradually focusing the graph representation from raw structural pattern $H({\mathcal{G}})$ to task-relevant information $H(Y_1)$.
  • Figure 2: IC curve in the original label task.
  • Figure 3: Summary of relative performance on all tasks.
  • Figure 4: Pruning process on the Karate Club network. Node colors denote ground-truth community labels.
  • Figure 5: Multi-step pruning by IGPrune on two microbial gene co-occurrence networks from Mount Everest (ME) and the Mariana Trench (MT). Each subplot shows network snapshots with $2,000+$ (raw), $1,000$, $300$, and $100$ edges.
  • ...and 1 more figures

Theorems & Definitions (7)

  • definition 1: Graph Semantics
  • Proposition 1: Predictor-Based Mutual Information Lower Bound
  • Remark 1
  • definition 2: Complexity Score
  • definition 3: Information Score
  • definition 4: Task-Relevant Graph Pruning Objective
  • Proposition 2: Predictor-Based Mutual Information Lower Bound