Efficient Algorithms for Computing Random Walk Centrality

TL;DR

This paper introduces two scalable algorithms for efficiently computing random walk centrality in large networks, significantly reducing computational costs while maintaining high approximation accuracy.

Contribution

The paper presents novel near-linear time algorithms for random walk centrality, utilizing approximate Cholesky factorization and spanning tree sampling, enabling analysis of massive networks.

Findings

Algorithms operate in near-linear time.

High approximation accuracy demonstrated on large networks.

Effective for networks with over 10 million nodes.

Abstract

Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph structural information and its wide range of applications, computing this measure for large networks remains impractical due to the computational demands of existing methods. In this paper, we present a novel formulation of random walk centrality, underpinning two scalable algorithms: one leveraging approximate Cholesky factorization and sparse inverse estimation, while the other sampling rooted spanning trees. Both algorithms operate in near-linear time and provide strong approximation guarantees. Extensive experiments on large real-world networks, including one with over 10 million nodes, demonstrate the efficiency and approximation quality of the proposed algorithms.