🔍 Hypergraph Mining

📖 Surveys & Tutorials

📑 A Survey

• A Survey on Hypergraph Mining: Patterns, Tools, and Generators [Paper] [Supplementary Document]

🎓 Tutorials

• Mining of Real-world Hypergraphs: Patterns, Tools, and Generators [Website] [Video]

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⚙️ Tools

🔹 Null Models

ID	Name	Paper
N1	Configuration Model	Configuration Models of Random Hypergraphs
N2	Random Filling Model	-
N3	HyperCL	How do Hyperedges Overlap in Real-world Hypergraphs? Patterns, Measures, and Generators

🔹 Structural Elements

ID	Name	Paper
E1	Open and Closed Triangles	Simplicial Closure and Higher-order Link Prediction
E2	Higher-order Network Motifs	Higher-order Motif Analysis in Hypergraphs
E3	Hypergraph Motifs	Hypergraph Motifs: Concepts, Algorithms, and Discoveries
		Hypergraph Motifs and Their Extensions Beyond Binary
E4	Temporal Hypergraph Motifs	THyMe+: Temporal Hypergraph Motifs and Fast Algorithms for Exact Counting
		Temporal Hypergraph Motifs
E5	Ego-networks	Hypergraph Ego-networks and Their Temporal Evolution
E6	Multi-level Decomposition	Structural Patterns and Generative Models of Real-world Hypergraphs
E9	Hypercores	Neighborhood-based Hypergraph Core Decomposition
		Hypercore Decomposition for Non-Fragile Hyperedges: Concepts, Algorithms, Observations, and Applications
		Exploring Cohesive Subgraphs in Hypergraphs: The (k,g)-core Approach
		(k,q)-core Decomposition of Hypergraphs
		Hcore-Init: Neural Network Initialization based on Graph Degeneracy
		A Hypergraph Model for the Yeast Protein Complex Network
E10	Hypergraph Communities	Community Recovery in Hypergraphs
		Community Detection in Large Hypergraphs
		Testing Community Structures for Hypergraphs
E11	Other Dense Substructures	A New Dynamic Algorithm for Densest Subhypergraphs
		Maintaining Densest Subsets Efficiently in Evolving Hypergraphs
		Densest Subhypergraph: Negative Supermodular Functions and Strongly Localized Methods
		A Survey on the Densest Subgraph Problem and Its Variants
		Identifying Maximal Sets of Significantly Interacting Nodes in Higher-order Networks
		The Generalized Mean Densest Subgraph Problem

🔹 Structural Quantities

ID	Name	Paper
Q1	Group Degrees	How do Hyperedges Overlap in Real-world Hypergraphs? Patterns, Measures, and Generators
Q2	Hypercoreness	Hypercore Decomposition for Non-Fragile Hyperedges: Concepts, Algorithms, Observations, and Applications
Q3	Distances	Distances in Higher-Order Networks and the Metric Structure of Hypergraphs
		Computation of Node Distances on Hypergraphs
		Hypernetwork Science via High-order Hypergraph Walks
		Hyper-distance Oracles in Hypergraphs
		Subgraph Centrality and Clustering in Complex Hyper-networks
		Almost Linear-time Algorithms for Adaptive Betweenness Centrality Using Hypergraph Sketches
Q4	Other Centrality Scores	Three Hypergraph Eigenvector Centralities
		Vector Centrality in Hypergraphs
		Node and Edge Nonlinear Eigenvector Centrality for Hypergraphs
		Vital Node Identification in Hypergraphs via Gravity Model
		Identifying Vital Nodes in Hypergraphs Based on Von Neumann Entropy
Q5	Hyperedge Homogeneity	How do Hyperedges Overlap in Real-world Hypergraphs? Patterns, Measures, and Generators
Q6	Transitivity	Clustering Coefficients in Protein Interaction Hypernetworks
		How Transitive Are Real-World Group Interactions? -- Measurement and Reproduction
		Hypergraphs and Cellular Networks
		The Why, How, and When of Representations for Complex Systems
Q7	Assortativity	Hypergraph Assortativity: A Dynamical Systems Perspective
Q8	Simpliciality	The Simpliciality of Higher-order Networks
Q9	Characteristic Profiles (CPs)	Superfamilies of Evolved and Designed Networks
		Hypergraph Motifs: Concepts, Algorithms, and Discoveries
Q10	Density	Complex Networks as Hypergraphs
		Maintaining Densest Subsets Efficiently in Evolving Hypergraphs
Q11	Overlapness	How do Hyperedges Overlap in Real-world Hypergraphs? Patterns, Measures, and Generators
Q12	Hypergraph Cuts	More Recent Advances in (Hyper)Graph Partitioning
		Hypergraph Partitioning for Multiple Communication Cost Metrics: Model and Methods
		Hypergraph Random Walks, Laplacians, and Clustering
		Network Flow-Based Refinement for Multilevel Hypergraph Partitioning
		Modeling Hypergraphs by Graphs with the Same Mincut Properties
		Learning with Hypergraphs: Clustering, Classification, and Embedding
		Minimizing Localized Ratio Cut Objectives in Hypergraphs
		Scalable High-Quality Hypergraph Partitioning
		High-Quality Hypergraph Partitioning
Q13	Conductance	Hypergraph Clustering Based on PageRank
Q14	Modularity	Preferential Attachment Hypergrpah with High Modularity
		Clustering via Hypergraph Modularity
		Towards Community Detection in k-Partite k-Uniform Hypergraphs
		Hypergraph Partitioning for Social Networks Based on Information Entropy Modularity
		Configuration Models of Random Hypergraphs
Q15	Persistence	On the Persistence of Higher-Order Interactions in Real-World Hypergraphs
Q16	Average Intersection Size	Hypergraph Ego-networks and Their Temporal Evolution
Q17	Effective Diameter	Evolution of Real-world Hypergraphs: Patterns and Models without Oracles

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📐 Patterns

🔹 Static Patterns

P1	Heavy-Tailed Degree Distributions	Evolution of Real-world Hypergraphs: Patterns and Models without Oracles
P2	Heavy-Tailed Hypercoreness Distributions	Hypercore Decomposition for Non-Fragile Hyperedges: Concepts, Algorithms, Observations, and Applications
P3	Core-Periphery Structures	Planted Hitting Set Recovery in Hypergraphs
		Core-periphery Models for Hypergraphs
		Core-periphery Detection in Hypergraphs
P4	Heavy-Tailed Size Distributions	Evolution of Real-world Hypergraphs: Patterns and Models without Oracles
P5	High Homogeneity	How do Hyperedges Overlap in Real-world Hypergraphs? Patterns, Measures, and Generators
P6	Substantial Encapsulation	Encapsulation Structure and Dynamics in Hypergraphs
P7	Heavy-Tailed Group Degree Distributions	A New Dynamic Algorithm for Densest Subhypergraphs
		How do Hyperedges Overlap in Real-world Hypergraphs? Patterns, Measures, and Generators
		Structural Patterns and Generative Models of Real-world Hypergraphs
P8	Heavy-Tailed Intersection Size Distributions	Evolution of Real-world Hypergraphs: Patterns and Models without Oracles
P9	Substantial Higher-Order Connectivity	Higher-order Components in Hypergrpahs
P10	High Transitivity	How Transitive Are Real-World Group Interactions? -- Measurement and Reproduction
		Structural Patterns and Generative Models of Real-world Hypergraphs
		Clustering Coefficients for Networks with Higher Order Interactions
P11	Densely Overlapping Ego-Networks	How do Hyperedges Overlap in Real-world Hypergraphs? Patterns, Measures, and Generators
P12	Community Structures	Inference of Hyperedges and Overlapping Communities in Hypergraphs
		Hyperlink Communities in Higher-order Networks
		The Why, How, and When of Representations for Complex Systems
P13	Dense Subhypergraphs	Sequences of Sets
		How do Hyperedges Overlap in Real-world Hypergraphs? Patterns, Measures, and Generators
		Configuration Models of Random Hypergraphs
P14	Strong Characterizing Power of Patterns	Simplicial Closure and Higher-order Link Prediction
		Higher-order Motif Analysis in Hypergraphs
		Hypergraph Patterns and Collaboration Structure
		Hypergraph Motifs: Concepts, Algorithms, and Discoveries
		Encapsulation Structure and Dynamics in Hypergraphs
		The Simpliciality of Higher-order Networks
P15	Strong Characterizing Power of Patterns	Evolution of Real-world Hypergraphs: Patterns and Models without Oracles
		Structural Patterns and Generative Models of Real-world Hypergraphs

🔹 Dynamic Patterns

P16	Frequent Hyperedge Repetitions	Sequences of Sets
		THyMe+: Temporal Hypergraph Motifs and Fast Algorithms for Exact Counting
		Temporal Hypergraph Motifs
		Temporal Properties of Higher-order Interactions in Social Networks
P17	Temporal Locality	Sequences of Sets
		Higher-Order Correlations Reveal Complex Memory in Temporal Hypergrpahs
P18	Temporal Reinforcement	Temporal Properties of Higher-order Interactions in Social Networks
P19	Power-Law Persistence	On the Persistence of Higher-Order Interactions in Real-World Hypergraphs
P20	Simplicial Closure	Simplicial Closure and Higher-order Link Prediction
P21	Temporal Locality in Ego-Networks	Hypergraph Ego-networks and Their Temporal Evolution
P22	Anthropic Principles of Ego-Networks	Hypergraph Ego-networks and Their Temporal Evolution
P23	Novelty-Rate Patterns of Ego-Networks	Hypergraph Ego-networks and Their Temporal Evolution
P24	Strong Characterizing Power of TH-Motifs	THyMe+: Temporal Hypergraph Motifs and Fast Algorithms for Exact Counting
		Temporal Hypergraph Motifs
P25	Diminishing Overlaps	Evolution of Real-world Hypergraphs: Patterns and Models without Oracles
P26	Densification	Evolution of Real-world Hypergraphs: Patterns and Models without Oracles
P27	Shrinking Diameter	Evolution of Real-world Hypergraphs: Patterns and Models without Oracles

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🛠️ Generators

🔹 Full-Hypergraph

G1	HyperLap	How do Hyperedges Overlap in Real-world Hypergraphs? Patterns, Measures, and Generators
G2	CIGAM	Core-periphery Models for Hypergraphs
G3	Hyper-dK	Randomizing Hypergraphs Preserving Degree Correlation and Local Clustering
G4	AMHM	Hypergraph Assortativity: A Dynamical Systems Perspective
G5	HSBM	Consistency of Spectral Hypergraph Partitioning under Planted Partition Model
G6	RNHM	Contagion Dynamics on Hypergraphs with Nested Hyperedges
G7	HOC	Higher-order Components in Hypergrpahs
G8	HyperPA	Structural Patterns and Generative Models of Real-world Hypergraphs
G9	HMPA	Preferential Attachment Hypergrpah with High Modularity
G10	HyperFF	Evolution of Real-world Hypergraphs: Patterns and Models without Oracles
G11	THera	How Transitive Are Real-World Group Interactions? -- Measurement and Reproduction
G12	DARH	Higher-Order Correlations Reveal Complex Memory in Temporal Hypergrpahs
G13	MiDaS	MiDaS: Representative Sampling from Real-world Hypergraphs
		Representative and Back-In-Time Sampling from Real-world Hypergraphs
G14	HRW	Efficiently Sampling and Estimating Hypergraphs By Hybrid Random Walk
G15	TRHC	Hypergraph Ego-networks and Their Temporal Evolution
G16	CRU	Sequences of Sets