Searching Personalized $k$-wing in Bipartite Graphs

Abidi, Aman; Chen, Lu; Zhou, Rui; Liu, Chengfei

doi:10.1109/tkde.2022.3199592

Cited by 5 publications

(2 citation statements)

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“…There have been several studies on counting triangles in unipartite graphs, including [32][33][34][35]. Since the butterfly is comparable to a triangle in a unipartite graph and serves as the smallest unit of cohesion in bipartite graphs [4], it is natural to consider leveraging the existing algorithms for triangle counting to count butterflies. However, butterfly counting in bipartite graphs presents significant challenges due to two key reasons.…”

Section: Related Workmentioning

confidence: 99%

“…Mining bipartite cohesive subgraphs, such as k-wing, maximal biclique, k-bitruss, balanced maximal biclique, etc., have attracted a lot of attention due to its wide range of applications across various domains such as community detection [1,2], finding highly collaborative research groups [3], and personalized recommendations [4]. A rectangle [5], butterfly, or 4-cycle [6] (i.e., a 2 × 2 complete bipartite subgraph) is the smallest subgraph that forms the basic building block of many bipartite cohesive subgraphs.…”

Section: Introductionmentioning

confidence: 99%

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Balanced Butterfly Counting in Bipartite-Network

Das,

Abidi,

Kiran

et al. 2024

Preprint

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Bipartite graphs offer a powerful framework for modeling complex relationshipsbetween two distinct types of vertices, incorporating probabilistic, temporal, andrating-based information. While the research community has extensively exploredvarious types of bipartite relationships, there has been a notable gap in studyingSigned Bipartite Graphs, which capture liking/ disliking interactions in real-worldnetworks such as customer-rating-product and senator-vote-bill. Balance but-terflies, representing 2 × 2 bicliques, provide crucial insights into antagonisticgroups, balance theory, and fraud detection by leveraging the signed information.However, such applications require counting balance butterflies which remainsunexplored. In this paper, we propose a new problem: counting balance butterfliesin a signed bipartite graph. To address this problem, we adapt state-of-the-artalgorithms for butterfly counting, establishing a smart baseline that reduces thetime complexity for solving our specific problem. We further introduce a novelbucket approach specifically designed to count balanced butterflies efficiently. Wepropose a parallelized version of the bucketing approach to enhance performance.Extensive experimental studies on nine real-world datasets demonstrate that ourproposed bucket-based algorithm is up to 120x faster over the baseline, and theparallel implementation of the bucket-based algorithm is up to 45x faster over thesingle core execution. Moreover, a real-world case study showcases the practicalapplication and relevance of counting balanced butterflies.

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