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How Do Hyperedges Overlap in Real-World Hypergraphs? -- Patterns, Measures, and Generators
Social and Information Networks · Submitted 19 Jan 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim HyperLap is (a) Realistic: it accurately reproduces overlapping patterns of real-world hypergraphs, (b) Automatically Fittable: its parameters can be tuned automatically using HyperLap+ to generate hypergraphs particularly similar to a given target hypergraph, (c) Scalable: it generates and fits a hypergraph with 0.7 billion hyperedges within a few hours.
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The abstract, sentence by sentence
Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in the number of nodes in each hyperedge, which provides the expressiveness of hypergraphs, brings about structural differences between graphs and hypergraphs. Especially, the overlaps of hyperedges lead to complex high-order relations beyond pairwise relations, raising new questions that have not been considered in graphs: How do hyperedges overlap in real-world hypergraphs? Are there any pervasive characteristics? What underlying process can cause such patterns? In this work, we closely investigate thirteen real-world hypergraphs from various domains and share interesting observations of overlaps of hyperedges. To this end, we define principled measures and statistically compare the overlaps of hyperedges in real-world hypergraphs and those in null models. Additionally, based on the observations, we propose HyperLap, a realistic hypergraph generative model. HyperLap is (a) Realistic: it accurately reproduces overlapping patterns of real-world hypergraphs, (b) Automatically Fittable: its parameters can be tuned automatically using HyperLap+ to generate hypergraphs particularly similar to a given target hypergraph, (c) Scalable: it generates and fits a hypergraph with 0.7 billion hyperedges within a few hours.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | The flexibility in the number of nodes in each hyperedge, which provides the expressiveness of hypergraphs, brings about structural differences between graphs and hypergraphs. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s2 | Especially, the overlaps of hyperedges lead to complex high-order relations beyond pairwise relations, raising new questions that have not been considered in graphs: How do hyperedges overlap in real-world hypergraphs? | gap 0.84 | 0.07 | 0.05 | asserted 0.99 |
| s3 | Are there any pervasive characteristics? | gap 0.91 | 0.03 | 0.02 | unclear 0.96 |
| s4 | What underlying process can cause such patterns? | gap 0.93 | 0.04 | 0.02 | unclear 0.97 |
| s5 | In this work, we closely investigate thirteen real-world hypergraphs from various domains and share interesting observations of overlaps of hyperedges. | contribution 0.72 | 0.97 | 0.09 | asserted 1.00 |
| s6 | To this end, we define principled measures and statistically compare the overlaps of hyperedges in real-world hypergraphs and those in null models. | method 0.96 | 0.96 | 0.05 | asserted 0.98 |
| s7 | Additionally, based on the observations, we propose HyperLap, a realistic hypergraph generative model. | contribution 0.76 | 0.94 | 0.15 | asserted 1.00 |
| s8 | HyperLap is (a) Realistic: it accurately reproduces overlapping patterns of real-world hypergraphs, (b) Automatically Fittable: its parameters can be tuned automatically using HyperLap+ to generate hypergraphs particularly similar to a given target hypergraph, (c) Scalable: it generates and fits a hypergraph with 0.7 billion hyperedges within a few hours. | contribution 0.61 | 0.93 | 0.27 | asserted 1.00 |
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Original abstract
Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in the number of nodes in each hyperedge, which provides the expressiveness of hypergraphs, brings about structural differences between graphs and hypergraphs. Especially, the overlaps of hyperedges lead to complex high-order relations beyond pairwise relations, raising new questions that have not been considered in graphs: How do hyperedges overlap in real-world hypergraphs? Are there any pervasive characteristics? What underlying process can cause such patterns? In this work, we closely investigate thirteen real-world hypergraphs from various domains and share interesting observations of overlaps of hyperedges. To this end, we define principled measures and statistically compare the overlaps of hyperedges in real-world hypergraphs and those in null models. Additionally, based on the observations, we propose HyperLap, a realistic hypergraph generative model. HyperLap is (a) Realistic: it accurately reproduces overlapping patterns of real-world hypergraphs, (b) Automatically Fittable: its parameters can be tuned automatically using HyperLap+ to generate hypergraphs particularly similar to a given target hypergraph, (c) Scalable: it generates and fits a hypergraph with 0.7 billion hyperedges within a few hours.
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Lee et al. [ref] extend the Chung-Lu model [ref] to hypergraphs (HyperCL) by ensuring to preserve the distribution from the given degree sequence and the edge-size sequence as input.
Higher-Order Networks Representation and Learning: A Survey · Generative Models · 0.99
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