Wedge Sampling for Computing Clustering Coefficients and Triangle Counts on Large Graphs

TL;DR

This paper introduces wedge sampling, a fast and accurate method for estimating clustering coefficients and triangle counts in large graphs, outperforming existing techniques in speed and accuracy.

Contribution

It presents a novel wedge sampling approach that improves the efficiency and accuracy of triangle and clustering coefficient estimations in large-scale graphs.

Findings

Wedge sampling provides faster approximations than previous methods.

The approach yields more accurate estimates with probabilistic error bounds.

Methods are validated with extensive experiments showing superior performance.

Abstract

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social cohesion. Algorithms to compute them can be extremely expensive, even for moderately-sized graphs with only millions of edges. Previous work has considered node and edge sampling; in contrast, we consider wedge sampling, which provides faster and more accurate approximations than competing techniques. Additionally, wedge sampling enables estimation local clustering coefficients, degree-wise clustering coefficients, uniform triangle sampling, and directed triangle counts. Our methods come with provable and practical probabilistic error estimates for all computations. We provide extensive results that show our methods are both more accurate and faster than state-of-the-art alternatives.