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The number of triangles in a graph is useful to deduce a plethora ofimportant features of the network that the graph is modeling. However, findingthe exact value of this number is computationally expensive. Hence, a number ofapproximation algorithms based on random sampling of edges, or wedges (adjacentedge pairs) have been proposed for estimating this value. We argue that forlarge sparse graphs with power-law degree distribution, random edge samplingrequires sampling large number of edges before providing enough information foraccurate estimation, and existing wedge sampling methods lead to biasedsamplings, which in turn lead to less accurate estimations. In this paper, wepropose a hybrid algorithm between edge and wedge sampling that addresses thedeficiencies of both approaches. We start with uniform edge sampling and thenextend each selected edge to form a wedge that is more informative forestimating the overall triangle count. The core estimate we make is the numberof triangles each sampled edge in the first phase participates in. Thisapproach provides accurate approximations with very small sampling ratios,outperforming the state-of-the-art up to 8 times in sample size while providingestimations with 95% confidence.

Edge-Based Wedge Sampling to Estimate Triangle Counts in Very Large Graphs