From Graphs to Hypergraphs: Hypergraph Projection and its Remediation

• URL: http://arxiv.org/abs/2401.08519v1
• Date: Tue, 16 Jan 2024 17:31:54 GMT
• Title: From Graphs to Hypergraphs: Hypergraph Projection and its Remediation
• Authors: Yanbang Wang, Jon Kleinberg
• Abstract summary: We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems. We develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions.
• Score: 2.0590577326314787
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

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