Fast Unbiased Sampling of Networks with Given Expected Degrees and Strengths

2025-09-16

AI Summary

Existing Chung–Lu models systematically overestimate edges between high-degree nodes, inducing bias in network statistical inference; while the maximum-entropy configuration model is theoretically unbiased, its high computational complexity renders it impractical. This paper introduces the first efficient, unbiased sampling framework for configuration models: we adapt the Miller–Hagberg algorithm to the maximum-entropy setting for the first time, incorporating both degree and strength constraints. Our method preserves theoretical unbiasedness while achieving substantial efficiency gains. Evaluated on 103 real-world networks, it delivers 10–1000× speedup over baseline approaches, enabling scalable unbiased network sampling at unprecedented scale. By reconciling statistical accuracy with computational feasibility, our work establishes a reliable, scalable foundation for rigorous network structure analysis.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The configuration model is a cornerstone of statistical assessment of network structure. While the Chung-Lu model is among the most widely used configuration models, it systematically oversamples edges between large-degree nodes, leading to inaccurate statistical conclusions. Although the maximum entropy principle offers unbiased configuration models, its high computational cost has hindered widespread adoption, making the Chung-Lu model an inaccurate yet persistently practical choice. Here, we propose fast and efficient sampling algorithms for the max-entropy-based models by adapting the Miller-Hagberg algorithm. Evaluation on 103 empirical networks demonstrates 10-1000 times speedup, making theoretically rigorous configuration models practical and contributing to a more accurate understanding of network structure.

Problem

• Unbiased sampling for networks with expected degrees
• Overcoming Chung-Lu model's systematic oversampling bias
• Reducing computational cost of max-entropy configuration models

Innovation

• Fast sampling for max-entropy models
• Adapting Miller-Hagberg algorithm approach
• Achieves 10-1000 times speedup performance