Abstract
This work focuses on distributions of triangle counts per node 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. Suitable sampling schemes for this are introduced and also adapted to the situations where network access is restricted or streaming data of edges are available. Estimation under the proposed sampling schemes is studied through several methods, and examined on simulated and real-world networks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Al Hasan, M., Dave, V.S.: Triangle counting in large networks: a review. WIREs Data Mining Knowl. Discov. 8(2), e1226 (2018)
Antunes, N., Pipiras, V.: Estimation of flow distributions from sampled traffic. ACM Trans. Model Perform. Eval. Comput. Syst. 1(3), 11:1–11:28 (2016)
Bar-Yossef, Z., Kumar, R., Sivakumar, D.: Reductions in streaming algorithms, with an application to counting triangles in graphs. In: Proceedings of the 13th Annual ACM-SIAM SODA, pp. 623–632 (2002)
Becchetti, L., Castillo, C., Donato, D., Baeza-YATES, R., Leonardi, S.: Link analysis for web spam detection. ACM Trans. Web 2(1), 2:1–2:42 (2008)
Buriol, L.S., Frahling, G., Leonardi, S., Marchetti-Spaccamela, A., Sohler, C.: Counting triangles in data streams. In: Proceedings of the 25th ACM SIGMOD-SIGACT-SIGART PODS, pp. 253–262 (2006)
Eckmann, J.-P., Moses, E.: Curvature of co-links uncovers hidden thematic layers in the world wide web. Proc. Natl. Acad. Sci. 99(9), 5825–5829 (2002)
Eldar, Y.C.: Generalized SURE for exponential families: applications to regularization. IEEE Trans. Signal Process. 57(2), 471–481 (2009)
Jha, M., Seshadhri, C., Pinar, A.: A space-efficient streaming algorithm for estimating transitivity and triangle counts using the birthday paradox. ACM Trans. Knowl. Discov. Data 9(3), 15:1–15:21 (2015)
Kolaczyk, E.D.: Statistical Analysis of Network Data. Springer, New York (2009). https://doi.org/10.1007/978-0-387-88146-1
Lim, Y., Jung, M., Kang, U.: Memory-efficient and accurate sampling for counting local triangles in graph streams: from simple to multigraphs. ACM Trans. Knowl. Discov. Data 12(1), 4:1–4:28 (2018)
Newman, M.: Networks: An Introduction, 2nd edn. Oxford University Press Inc., New York (2018)
Palla, G., Derényi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043), 814–818 (2005)
Stefani, L.D., Epasto, A., Riondato, M., Upfal, E.: TriÈst: counting local and global triangles in fully dynamic streams with fixed memory size. ACM Trans. Knowl. Discov. Data 11(4), 43:1–43:50 (2017)
Tune, P., Veitch, D.: Fisher information in flow size distribution estimation. IEEE Trans. Info. Theory 57(10), 7011–7035 (2011)
Vitter, J.S.: Random sampling with a reservoir. ACM Trans. Math. Softw. 1(1), 37–57 (1985)
Zhang, Y., Kolaczyk, E.D., Spencer, B.D.: Estimating network degree distributions under sampling: an inverse problem, with applications to monitoring social media networks. Ann. Appl. Stat. 9(1), 166–199 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Antunes, N., Guo, T., Pipiras, V. (2020). Induced Edge Samplings and Triangle Count Distributions in Large Networks. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 882. Springer, Cham. https://doi.org/10.1007/978-3-030-36683-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-36683-4_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-36682-7
Online ISBN: 978-3-030-36683-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)