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Sampling methods and estimation of triangle count distributions in large networks

Published online by Cambridge University Press:  26 February 2021

Nelson Antunes Open the ORCID record for Nelson Antunes [Opens in a new window] ,
Tianjian Guo  and
Vladas Pipiras
Nelson Antunes*
Affiliation:
Center for Computational and Stochastic Mathematics, University of Lisbon, Avenida Rovisco Pais 1049-001, Lisbon, Portugal University of Algarve, Faro, Portugal
Tianjian Guo
Affiliation:
Department of Statistics and Operations Research, University of North Carolina, CB 3260, Chapel Hill, NC 27599, USA (e-mails: Tianjian.Guo@mccombs.utexas.edu, pipiras@email.unc.edu)
Vladas Pipiras
Affiliation:
Department of Statistics and Operations Research, University of North Carolina, CB 3260, Chapel Hill, NC 27599, USA (e-mails: Tianjian.Guo@mccombs.utexas.edu, pipiras@email.unc.edu)
*
*Corresponding author. Email: nantunes@ualg.pt
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Abstract

This paper investigates the distributions of triangle counts per vertex and edge, as a means for network description, analysis, model building, and other tasks. The main interest is in estimating these distributions through sampling, especially for large networks. A novel sampling method tailored for the estimation analysis is proposed, with three sampling designs motivated by several network access scenarios. An estimation method based on inversion and an asymptotic method are developed to recover the entire distribution. A single method to estimate the distribution using multiple samples is also considered. Algorithms are presented to sample the network under the various access scenarios. Finally, the estimation methods on synthetic and real-world networks are evaluated in a data study.

Keywords

trianglesrandom samplingdistribution estimationinversion approachasymptotic approachmultiple samplesstatic and streaming graphspower laws
Type
Research Article
Information
Network Science , Volume 9 , Special Issue S1: Complex Networks 2019 , October 2021 , pp. S134 - S156
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

Action Editor: Hocine Cherifi

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