Closed Walk Sampler: An Efficient Method for Estimating Eigenvalues of Large Graphs

TL;DR

This paper introduces a new sampling algorithm that efficiently estimates the two largest eigenvalues of large graphs using random walks and closed walk counts, outperforming existing methods in speed and accuracy.

Contribution

The paper presents a novel sampling approach that estimates top eigenvalues of large graphs by counting closed walks, reducing computational costs compared to traditional eigenvalue algorithms.

Findings

Algorithms are significantly faster than existing methods.

Achieve higher accuracy in eigenvalue estimation.

Effective on real-world large graphs.

Abstract

Eigenvalues of a graph are of high interest in graph analytics for Big Data due to their relevance to many important properties of the graph including network resilience, community detection and the speed of viral propagation. Accurate computation of eigenvalues of extremely large graphs is usually not feasible due to the prohibitive computational and storage costs and also because full access to many social network graphs is often restricted to most researchers. In this paper, we present a series of new sampling algorithms which solve both of the above-mentioned problems and estimate the two largest eigenvalues of a large graph efficiently and with high accuracy. Unlike previous methods which try to extract a subgraph with the most influential nodes, our algorithms sample only a small portion of the large graph via a simple random walk, and arrive at estimates of the two largest eigenvalues by estimating the number of closed walks of a certain length. Our experimental results using real graphs show that our algorithms are substantially faster while also achieving significantly better accuracy on most graphs than the current state-of-the-art algorithms.