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Scalable Approximate Butterfly and Bi-triangle Counting for Large Bipartite Networks

Authors:

Fangyuan Zhang,

Junhao GanAuthors Info & Claims

Proceedings of the ACM on Management of Data, Volume 1, Issue 4

Article No.: 259, Pages 1 - 26

https://doi.org/10.1145/3626753

Published: 12 December 2023 Publication History

Abstract

A bipartite graph is a graph that consists of two disjoint sets of vertices and only edges between vertices from different vertex sets. In this paper, we study the counting problems of two common types of em motifs in bipartite graphs: (i) butterflies (2x2 bicliques) and (ii) bi-triangles (length-6 cycles). Unlike most of the existing algorithms that aim to obtain exact counts, our goal is to obtain precise enough estimations of these counts in bipartite graphs, as such estimations are already sufficient and of great usefulness in various applications. While there exist approximate algorithms for butterfly counting, these algorithms are mainly based on the techniques designed for general graphs, and hence, they are less effective on bipartite graphs. Not to mention that there is still a lack of study on approximate bi-triangle counting. Motivated by this, we first propose a novel butterfly counting algorithm, called one-sided weighted sampling, which is tailored for bipartite graphs. The basic idea of this algorithm is to estimate the total butterfly count with the number of butterflies containing two randomly sampled vertices from the same side of the two vertex sets. We prove that our estimation is unbiased, and our technique can be further extended (non-trivially) for bi-triangle count estimation. Theoretical analyses under a power-law random bipartite graph model and extensive experiments on multiple large real datasets demonstrate that our proposed approximate counting algorithms can reach high accuracy, yet achieve up to three orders (resp. four orders) of magnitude speed-up over the state-of-the-art exact butterfly (resp. bi-triangle) counting algorithms. Additionally, we present an approximate clustering coefficient estimation framework for bipartite graphs, which shows a similar speed-up over the exact solutions with less than 1% relative error.

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Index Terms

Scalable Approximate Butterfly and Bi-triangle Counting for Large Bipartite Networks
1. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

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cover image Proceedings of the ACM on Management of Data

Proceedings of the ACM on Management of Data Volume 1, Issue 4

PACMMOD

December 2023

1317 pages

EISSN:2836-6573

DOI:10.1145/3637468

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Divyakant Agrawal
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Published: 12 December 2023

Published in PACMMOD Volume 1, Issue 4

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https://dl.acm.org/doi/10.14778/3641204.3641215
Mai GHe ZYu GChen ZChen P(2024)CTuner: Automatic NoSQL Database Tuning with Causal Reinforcement LearningProceedings of the 15th Asia-Pacific Symposium on Internetware10.1145/3671016.3674809(269-278)Online publication date: 24-Jul-2024
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Sun GZhao YLi YSerra ESpezzano F(2024)FABLE: Approximate Butterfly Counting in Bipartite Graph Stream with Duplicate EdgesProceedings of the 33rd ACM International Conference on Information and Knowledge Management10.1145/3627673.3679812(2158-2167)Online publication date: 21-Oct-2024
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Wang ZLai LLiu YShui BTian CZhong S(2024)Parallelization of butterfly counting on hierarchical memoryThe VLDB Journal — The International Journal on Very Large Data Bases10.1007/s00778-024-00856-x33:5(1453-1484)Online publication date: 1-Sep-2024
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