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Provable and Practical Approximations for the Degree Distribution using Sublinear Graph Samples

Authors:

C. SeshadhriAuthors Info & Claims

WWW '18: Proceedings of the 2018 World Wide Web Conference

April 2018

Pages 449 - 458

https://doi.org/10.1145/3178876.3186111

Published: 23 April 2018 Publication History

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Abstract

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.

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Index Terms

Provable and Practical Approximations for the Degree Distribution using Sublinear Graph Samples
1. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
  2. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design
      1. Social networks

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cover image ACM Other conferences

WWW '18: Proceedings of the 2018 World Wide Web Conference

April 2018

2000 pages

ISBN:9781450356398

General Chairs:
Pierre-Antoine Champin
Universitè Claude Bernard Lyon 1, France
,
Fabien Gandon
Inria, Université Côte d'Azur, CNRS, I3S, France
,
Lionel Médini
Université Claude Bernard Lyon 1, France
,
Program Chairs:
Mounia Lalmas
Spotify, UK
,
Panagiotis G. Ipeirotis
New York University, USA

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IW3C2: International World Wide Web Conference Committee

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SIGWEB: ACM Special Interest Group on Hypertext, Hypermedia, and Web

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International World Wide Web Conferences Steering Committee

Republic and Canton of Geneva, Switzerland

Publication History

Published: 23 April 2018

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Funding Sources

Azrieli Foundation
Israel Science Foundation
Blavatnik fund
Laboratory Directed Research and Development program at Sandia National Laboratories
NSF TRIPODS
Simons Institute

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WWW '18

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IW3C2

WWW '18: The Web Conference 2018

April 23 - 27, 2018

Lyon, France

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WWW '18 Paper Acceptance Rate 170 of 1,155 submissions, 15%;

Overall Acceptance Rate 1,899 of 8,196 submissions, 23%

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https://dl.acm.org/doi/10.1145/3589334.3645551
Wang KLiang YLi XLi GGhanem BZimmermann RZhou ZYi HZhang YWang Y(2024)Brave the Wind and the Waves: Discovering Robust and Generalizable Graph Lottery TicketsIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2023.334218446:5(3388-3405)Online publication date: May-2024
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Zhang LLiu GLiu XWu J(2024)Denoising Item Graph With Disentangled Learning for RecommendationIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2024.336148236:7(2942-2955)Online publication date: Jul-2024
https://doi.org/10.1109/TKDE.2024.3361482
Zhang WOu WLi WGou JXiao WLiu B(2023)Robust Graph Structure Learning with Virtual Nodes ConstructionMathematics10.3390/math1106139711:6(1397)Online publication date: 13-Mar-2023
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