TY - GEN

T1 - Provable and practical approximations for the degree distribution using sublinear graph samples

AU - Eden, Talya

AU - Jain, Shweta

AU - Pinar, Ali

AU - Ron, Dana

AU - Seshadhri, C.

N1 - Publisher Copyright: © 2018 IW3C2 (International World Wide Web Conference Committee), published under Creative Commons CC BY 4.0 License.

PY - 2018/4/10

Y1 - 2018/4/10

N2 - The degree distribution is one of the most fundamental properties used in the analysis of massive graphs. There 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. Estimating the degree distribution of real-world graphs poses a significant challenge, due to their heavy-tailed nature and the large variance in degrees. We design a new algorithm, SADDLES, for this problem, using recent mathematical techniques from the field of sublinear algorithms. The SADDLES algorithm gives provably accurate outputs for all values of the degree distribution. For the analysis, we define 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. This 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.

AB - The degree distribution is one of the most fundamental properties used in the analysis of massive graphs. There 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. Estimating the degree distribution of real-world graphs poses a significant challenge, due to their heavy-tailed nature and the large variance in degrees. We design a new algorithm, SADDLES, for this problem, using recent mathematical techniques from the field of sublinear algorithms. The SADDLES algorithm gives provably accurate outputs for all values of the degree distribution. For the analysis, we define 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. This 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.

KW - Degree distribution

KW - Graphs

KW - Sampling

KW - Sublinear

UR - http://www.scopus.com/inward/record.url?scp=85061190097&partnerID=8YFLogxK

U2 - https://doi.org/10.1145/3178876.3186111

DO - https://doi.org/10.1145/3178876.3186111

M3 - منشور من مؤتمر

T3 - The Web Conference 2018 - Proceedings of the World Wide Web Conference, WWW 2018

SP - 449

EP - 458

BT - The Web Conference 2018 - Proceedings of the World Wide Web Conference, WWW 2018

T2 - 27th International World Wide Web, WWW 2018

Y2 - 23 April 2018 through 27 April 2018

ER -