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Graphs are used to model interactions in a variety of contexts, and there isa growing need to quickly assess the structure of a graph. Some of the mostuseful graph metrics, especially those measuring social cohesion, are based ontriangles. Despite the importance of these triadic measures, associatedalgorithms can be extremely expensive. We propose a new method based on wedgesampling. This versatile technique allows for the fast and accurateapproximation of all current variants of clustering coefficients and enablesrapid uniform sampling of the triangles of a graph. Our methods come withprovable and practical time-approximation tradeoffs for all computations. Weprovide extensive results that show our methods are orders of magnitude fasterthan the state-of-the-art, while providing nearly the accuracy of fullenumeration. Our results will enable more wide-scale adoption of triadicmeasures for analysis of extremely large graphs, as demonstrated on severalreal-world examples.

Triadic Measures on Graphs: The Power of Wedge Sampling