In this work, we present a new algorithm to approximate the percolation centrality of every node in a graph. Such a centrality measure quantifies the importance of the vertices in a network during a contagious process. In this paper, we present a randomized approximation algorithm that can compute probabilistically guaranteed high-quality percolation centrality estimates, generalizing techniques used by Pellegrina and Vandin (TKDD 2024) for the betweenness centrality. The estimation obtained by our algorithm is within $\varepsilon$ of the value with probability at least $1-\delta$, for fixed constants $\varepsilon,\delta \in (0,1)$. We our theoretical results with an extensive experimental analysis on several real-world networks and provide empirical evidence that our algorithm improves the current state of the art in speed, and sample size while maintaining high accuracy of the percolation centrality estimates.

翻译：本文提出了一种新的算法，用于近似计算图中每个节点的渗流中心性。该中心性度量量化了在传播过程中网络顶点的重要性。本文提出了一种随机近似算法，能够计算具有概率保证的高质量渗流中心性估计值，推广了Pellegrina和Vandin（TKDD 2024）用于中介中心性的技术。对于固定常数$\varepsilon,\delta \in (0,1)$，本算法获得的估计值以至少$1-\delta$的概率落在真实值的$\varepsilon$范围内。我们通过在多组真实世界网络上进行广泛的实验分析来验证理论结果，并提供经验证据表明，本算法在保持渗流中心性估计高精度的同时，在速度和样本量方面改进了当前技术水平。