Retrieving Top-k Hyperedge Triplets: Models and Applications

Conference · Tue Dec 31 04:00:00 EST 2024

DOI:https://doi.org/10.1109/BigData62323.2024.10825860· OSTI ID:2565827

Niu, Jason ^[1]; Amburg, Ilya D. ^[1]; Aksoy, Sinan G. ^[1]; Sariyuce, Ahmet Erdem ^[2]

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1. BATTELLE (PACIFIC NW LAB)
2. University at Buffalo

Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions can- not be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods that analyze hypergraphs directly, rather than via lossy graph reductions, remain limited. Hypergraph motifs hold promise in this regard, as motif patterns serve as building blocks for larger group interactions which are inexpressible by graphs. Recent work has focused on categorizing and counting hypergraph motifs based on the existence of nodes in hyperedge intersection regions. Here, we argue that the relative sizes of hyperedge inter- sections within motifs contain varied and valuable information. We propose a suite of efficient algorithms for finding top-k triplets of hyperedges based on optimizing the sizes of these intersection patterns. This formulation uncovers interesting local patterns of interaction, finding hyperedge triplets that either (1) are the least similar with each other, (2) have the highest pairwise but not groupwise correlation, or (3) are the most similar with each other. We formalize this as a combinatorial optimization problem and design efficient algorithms based on filtering hyperedges. Our comprehensive experimental evaluation shows that the resulting hyperedge triplets yield insightful information on real-world hypergraphs. Our approach is also orders of magnitude faster than a naive baseline implementation.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 2565827
• Report Number(s): PNNL-SA-191147
• Country of Publication: United States
• Language: English

Related Subjects

hypergraphs
motifs
Combinatorial Algorithms