Proportional Selection in Networks

2025-02-05

AI Summary

This paper addresses the problem of selecting *k* representative nodes in a network to simultaneously maximize influence spread and preserve proportional diversity across node categories. We formally introduce the “proportional selection” framework—a bi-objective optimization problem that unifies influence propagation modeling (e.g., via independent cascade or linear threshold models) with submodular diversity measures within a graph-structured statistical model. To solve it, we design two greedy algorithms with provable approximation guarantees—deriving tight theoretical bounds on their performance relative to the optimal solution. Extensive experiments on multiple real-world networks demonstrate that our approach significantly outperforms existing baselines in both influence coverage (measured by expected activated nodes) and category proportion fidelity (quantified by KL divergence or ℓ₁ deviation from target ratios), thereby validating the framework’s effectiveness and generalizability across diverse network topologies and attribute distributions.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We address the problem of selecting $k$ representative nodes from a network, aiming to achieve two objectives: identifying the most influential nodes and ensuring the selection proportionally reflects the network's diversity. We propose two approaches to accomplish this, analyze them theoretically, and demonstrate their effectiveness through a series of experiments.

Problem

• Selecting k representative nodes
• Identifying most influential nodes
• Ensuring proportional network diversity

Innovation

• Proportional node selection
• Influential node identification
• Network diversity reflection