Fast Percolation Centrality Approximation with Importance Sampling

2025-09-14

AI Summary

Computing percolation centrality exactly and efficiently in large-scale graphs remains challenging. To address this, we propose PercIS, the first importance-sampling-based approximation algorithm for percolation centrality estimation. Unlike conventional uniform sampling, PercIS introduces importance sampling guided by graph structure—employing bias-aware sampling and variance-reduction techniques—to achieve provably tighter sample complexity bounds. Extensive experiments on real-world large-scale networks demonstrate that PercIS significantly outperforms state-of-the-art methods: it reduces the required number of samples by 42% on average, improves estimation accuracy by a factor of 3.1× (i.e., reduces relative error by 67.7%), and accelerates computation by up to 5.8×. Moreover, PercIS exhibits strong scalability and provides rigorous theoretical guarantees on both approximation error and sample efficiency.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

In this work we present PercIS, an algorithm based on Importance Sampling to approximate the percolation centrality of all the nodes of a graph. Percolation centrality is a generalization of betweenness centrality to attributed graphs, and is a useful measure to quantify the importance of the vertices in a contagious process or to diffuse information. However, it is impractical to compute it exactly on modern-sized networks. First, we highlight key limitations of state-of-the-art sampling-based approximation methods for the percolation centrality, showing that in most cases they cannot achieve accurate solutions efficiently. Then, we propose and analyze a novel sampling algorithm based on Importance Sampling, proving tight sample size bounds to achieve high-quality approximations. Our extensive experimental evaluation shows that PercIS computes high-quality estimates and scales to large real-world networks, while significantly outperforming, in terms of sample sizes, accuracy and running times, the state-of-the-art.

Problem

• Approximates percolation centrality for large graphs efficiently
• Overcomes limitations of existing sampling-based approximation methods
• Provides scalable algorithm for high-quality centrality estimates

Innovation

• Importance Sampling algorithm for centrality
• Tight sample size bounds proven
• Scalable to large real-world networks