Triadic Measures on Graphs: The Power of Wedge Sampling

TL;DR

This paper introduces wedge sampling, a fast and accurate method for approximating triadic graph measures like clustering coefficients, significantly outperforming existing algorithms in speed while maintaining high accuracy.

Contribution

The authors present a novel wedge sampling technique that enables rapid approximation of triadic measures with provable accuracy and efficiency, facilitating analysis of large-scale graphs.

Findings

Wedge sampling is orders of magnitude faster than previous methods.

The technique provides nearly the same accuracy as full enumeration.

Applications on real-world graphs demonstrate scalability and effectiveness.

Abstract

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of a graph. Some of the most useful graph metrics, especially those measuring social cohesion, are based on triangles. Despite the importance of these triadic measures, associated algorithms can be extremely expensive. We propose a new method based on wedge sampling. This versatile technique allows for the fast and accurate approximation of all current variants of clustering coefficients and enables rapid uniform sampling of the triangles of a graph. Our methods come with provable and practical time-approximation tradeoffs for all computations. We provide extensive results that show our methods are orders of magnitude faster than the state-of-the-art, while providing nearly the accuracy of full enumeration. Our results will enable more wide-scale adoption of triadic measures for analysis of extremely large graphs, as demonstrated on several real-world examples.