Provable and practical approximations for the degree distribution using sublinear graph samples

Œe degree distribution is one of the most fundamental properties used in the analysis of massive graphs. Œere is a large literature on graph sampling, where the goal is to estimate properties (especially the degree distribution) of a large graph through a small, random sample. Œe degree distribution estimation poses a signi€cant challenge, due to its heavy-tailed nature and the large variance in degrees. We design a new algorithm, SADDLES, for this problem, using recent mathematical techniques from the €eld of sublinear algorithms. Œe SADDLES algorithm gives provably accurate outputs for all values of the degree distribution. For the analysis, we de€ne two fatness measures of the degree distribution, called the h-index and the z-index. We prove that SADDLES is sublinear in the graph size when these indices are large. A corollary of this result is a provably sublinear algorithm for any degree distribution bounded below by a power law. We deploy our new algorithm on a variety of real datasets and demonstrate its excellent empirical behavior. In all instances, we get extremely accurate approximations for all values in the degree distribution by observing at most 1% of the vertices. Œis is a major improvement over the state-of-the-art sampling algorithms, which typically sample more than 10% of the vertices to give comparable results. We also observe that the h and z-indices of real graphs are large, validating our theoretical analysis. ACM Reference format: Talya Eden, Shweta Jain, Ali Pinar, Dana Ron, and C. Seshadhri. 2016. Provable and practical approximations for the degree distribution using sublinear graph samples. In Proceedings of , , , 12 pages.