Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
156 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A Survey on Hypergraph Mining: Patterns, Tools, and Generators (2401.08878v1)

Published 16 Jan 2024 in cs.SI, cs.DB, and physics.soc-ph

Abstract: Hypergraphs are a natural and powerful choice for modeling group interactions in the real world, which are often referred to as higher-order networks. For example, when modeling collaboration networks, where collaborations can involve not just two but three or more people, employing hypergraphs allows us to explore beyond pairwise (dyadic) patterns and capture groupwise (polyadic) patterns. The mathematical complexity of hypergraphs offers both opportunities and challenges for learning and mining on hypergraphs, and hypergraph mining, which seeks to enhance our understanding of underlying systems through hypergraph modeling, gained increasing attention in research. Researchers have discovered various structural patterns in real-world hypergraphs, leading to the development of mining tools. Moreover, they have designed generators with the aim of reproducing and thereby shedding light on these patterns. In this survey, we provide a comprehensive overview of the current landscape of hypergraph mining, covering patterns, tools, and generators. We provide comprehensive taxonomies for them, and we also provide in-depth discussions to provide insights into future research on hypergraph mining.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (150)
  1. 2024. Supplementary Document for ‘A Survey on Hypergraph Mining: Patterns, Tools, and Generators’. http://dmlab.kaist.ac.kr/~kijungs/hypergraph_survey_supp.pdf.
  2. Community recovery in hypergraphs. IEEE Transactions on Information Theory 65, 10 (2019), 6561–6579.
  3. Oddball: Spotting anomalies in weighted graphs. In Advances in Knowledge Discovery and Data Mining: 14th Pacific-Asia Conference, PAKDD 2010, Hyderabad, India, June 21-24, 2010. Proceedings. Part II 14. Springer, 410–421.
  4. Graph based anomaly detection and description: a survey. Data mining and knowledge discovery 29 (2015), 626–688.
  5. Planted hitting set recovery in hypergraphs. Journal of Physics: Complexity 2, 3 (2021), 035004.
  6. Group recommendation: Semantics and efficiency. Proceedings of the VLDB Endowment 2, 1 (2009), 754–765.
  7. A Survey on Hypergraph Representation Learning. Comput. Surveys 56, 1 (2023), 1–38.
  8. Social influence maximization in hypergraphs. Entropy 23, 7 (2021), 796.
  9. Neighborhood-based Hypergraph Core Decomposition. Proceedings of the VLDB Endowment 16, 9 (2023), 2061–2074.
  10. Barry C Arnold. 2014. Pareto distribution. Wiley StatsRef: Statistics Reference Online (2014), 1–10.
  11. Hypersage: Generalizing inductive representation learning on hypergraphs. arXiv preprint arXiv:2010.04558 (2020).
  12. Applied probability and queues. Vol. 2. Springer.
  13. Albert-László Barabási and Réka Albert. 1999. Emergence of scaling in random networks. science 286, 5439 (1999), 509–512.
  14. Albert-László Barabási and Eric Bonabeau. 2003. Scale-free networks. Scientific american 288, 5 (2003), 60–69.
  15. Networks beyond pairwise interactions: Structure and dynamics. Physics Reports 874 (2020), 1–92.
  16. Simplicial closure and higher-order link prediction. Proceedings of the National Academy of Sciences 115, 48 (2018), E11221–E11230.
  17. Sequences of sets. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 1148–1157.
  18. Fast unfolding of communities in large networks. Journal of statistical mechanics: theory and experiment 2008, 10 (2008), P10008.
  19. Graph generators: State of the art and open challenges. ACM computing surveys 53, 2 (2020), 1–30.
  20. Stephen P Borgatti and Martin G Everett. 2000. Models of core/periphery structures. Social networks 21, 4 (2000), 375–395.
  21. Hypercore Decomposition for Non-Fragile Hyperedges: Concepts, Algorithms, Observations, and Applications. Data Mining and Knowledge Discovery 37 (2023), 2389 – 2437.
  22. More recent advances in (hyper) graph partitioning. Comput. Surveys 55, 12 (2023), 1–38.
  23. Detection of overlapping communities in dynamical social networks. In 2010 IEEE second international conference on social computing. IEEE, 309–314.
  24. Temporal properties of higher-order interactions in social networks. Scientific reports 11, 1 (2021), 1–10.
  25. Deepayan Chakrabarti. 2004. Autopart: Parameter-free graph partitioning and outlier detection. In European conference on principles of data mining and knowledge discovery. Springer, 112–124.
  26. Deepayan Chakrabarti and Christos Faloutsos. 2006. Graph mining: Laws, generators, and algorithms. ACM computing surveys 38, 1 (2006), 2–es.
  27. Lifting Markov chains to speed up mixing. In Proceedings of the thirty-first annual ACM symposium on Theory of computing. 275–281.
  28. Clustering large attributed graphs: A balance between structural and attribute similarities. ACM Transactions on Knowledge Discovery from Data 5, 2 (2011), 1–33.
  29. Community detection in hypergraphs: Optimal statistical limit and efficient algorithms. In International Conference on Artificial Intelligence and Statistics. PMLR, 871–879.
  30. Uthsav Chitra and Benjamin Raphael. 2019. Random Walks on Hypergraphs with Edge-Dependent Vertex Weights. In International conference on machine learning. PMLR, 1172–1181.
  31. Philip S Chodrow. 2020. Configuration models of random hypergraphs. Journal of Complex Networks 8, 3 (2020), cnaa018.
  32. Midas: Representative sampling from real-world hypergraphs. In Proceedings of the ACM Web Conference 2022. 1080–1092.
  33. Hyunjin Choo and Kijung Shin. 2022. On the persistence of higher-order interactions in real-world hypergraphs. In Proceedings of the 2022 SIAM International Conference on Data Mining. SIAM, 163–171.
  34. Random walk with restart on hypergraphs: fast computation and an application to anomaly detection. Data Mining and Knowledge Discovery (2023), 1–36.
  35. Fan Chung and Linyuan Lu. 2002. The average distances in random graphs with given expected degrees. PNAS 99, 25 (2002), 15879–15882.
  36. On community detection in real-world networks and the importance of degree assortativity. In Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining. 1007–1015.
  37. Cazamere Comrie and Jon Kleinberg. 2021. Hypergraph ego-networks and their temporal evolution. In 2021 IEEE international conference on data mining. IEEE, 91–100.
  38. Inference of hyperedges and overlapping communities in hypergraphs. Nature Communications 13, 1 (2022), 1–10.
  39. On positional and structural node features for graph neural networks on non-attributed graphs. In Proceedings of the 31st ACM International Conference on Information & Knowledge Management. 3898–3902.
  40. Luke L. B. Davis. 2021. ProPlot.
  41. Be More with Less: Hypergraph Attention Networks for Inductive Text Classification. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing. 4927–4936.
  42. Manh Tuan Do and Kijung Shin. 2023. Improving the core resilience of real-world hypergraphs. Data Mining and Knowledge Discovery 37, 6 (2023), 2438–2493.
  43. Structural patterns and generative models of real-world hypergraphs. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 176–186.
  44. Clustering large graphs via the singular value decomposition. Machine learning 56 (2004), 9–33.
  45. Mikhail Drobyshevskiy and Denis Turdakov. 2019. Random graph modeling: A survey of the concepts. ACM computing surveys 52, 6 (2019), 1–36.
  46. Provable and practical approximations for the degree distribution using sublinear graph samples. In Proceedings of the 2018 World Wide Web Conference. 449–458.
  47. Ego-net community mining applied to friend suggestion. Proceedings of the VLDB Endowment 9, 4 (2015), 324–335.
  48. Paul Erdős and Alfréd Rényi. 1960. On the evolution of random graphs. Publ. math. inst. hung. acad. sci 5, 1 (1960), 17–60.
  49. On power-law relationships of the internet topology. ACM SIGCOMM computer communication review 29, 4 (1999), 251–262.
  50. Hypergraph models of biological networks to identify genes critical to pathogenic viral response. BMC bioinformatics 22, 1 (2021), 1–21.
  51. Towards a survey on static and dynamic hypergraph visualizations. In 2021 IEEE visualization conference (VIS). IEEE, 81–85.
  52. Santo Fortunato. 2010. Community detection in graphs. Physics reports 486, 3-5 (2010), 75–174.
  53. Suzanne Renick Gallagher and Debra S Goldberg. 2013. Clustering coefficients in protein interaction hypernetworks. In Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics. 552–560.
  54. Higher-order correlations reveal complex memory in temporal hypergraphs. arXiv preprint arXiv:2303.09316 (2023).
  55. Hypergraph learning: Methods and practices. IEEE Transactions on Pattern Analysis and Machine Intelligence 44, 5 (2020), 2548–2566.
  56. Preferential attachment hypergraph with high modularity. Network Science 10, 4 (2022), 400–429.
  57. Hypergraphs and extremal optimization in 3D integrated circuit design automation. Advanced Engineering Informatics 33 (2017), 491–501.
  58. Real-time twitter recommendation: Online motif detection in large dynamic graphs. Proceedings of the VLDB Endowment 7, 13 (2014), 1379–1380.
  59. Clustering coefficients for networks with higher order interactions. arXiv preprint arXiv:2311.08563 (2023).
  60. Paul W Holland and Samuel Leinhardt. 1971. Transitivity in structural models of small groups. Comparative group studies 2, 2 (1971), 107–124.
  61. Maintaining densest subsets efficiently in evolving hypergraphs. In Proceedings of the 2017 ACM on Conference on Information and Knowledge Management. 929–938.
  62. Triadic closure pattern analysis and prediction in social networks. IEEE Transactions on Knowledge and Data Engineering 27, 12 (2015), 3374–3389.
  63. A space-efficient streaming algorithm for estimating transitivity and triangle counts using the birthday paradox. ACM Transactions on Knowledge Discovery from Data 9, 3 (2015), 1–21.
  64. Bepi: Fast and memory-efficient method for billion-scale random walk with restart. In Proceedings of the 2017 ACM International Conference on Management of Data. 789–804.
  65. Hypergraph patterns and collaboration structure. arXiv preprint arXiv:2210.02163 (2022).
  66. Clustering via hypergraph modularity. PloS one 14, 11 (2019), e0224307.
  67. Pegasus: mining peta-scale graphs. Knowledge and information systems 27 (2011), 303–325.
  68. Automated detection of influential patents using singular values. IEEE Transactions on Automation Science and Engineering 9, 4 (2012), 723–733.
  69. Contagion dynamics on hypergraphs with nested hyperedges. Physical Review E 108, 3 (2023), 034313.
  70. Jung-Ho Kim and K-I Goh. 2022. Higher-order components in hypergraphs. Bulletin of the American Physical Society 67 (2022).
  71. How Transitive Are Real-World Group Interactions?–Measurement and Reproduction. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 1132–1143.
  72. Reciprocity in directed hypergraphs: measures, findings, and generators. Data Mining and Knowledge Discovery 37, 6, 2330–2388.
  73. Hypergraphs and cellular networks. PLoS computational biology 5, 5 (2009), e1000385.
  74. Growth patterns and models of real-world hypergraphs. KAIS 64, 11 (2022), 2883–2920.
  75. Exploiting in-hub temporal locality in SpMV-based graph processing. In Proceedings of the 50th International Conference on Parallel Processing. 1–10.
  76. LOTUS: Locality optimizing triangle counting. In ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming. 219–233.
  77. Evolution of real-world hypergraphs: Patterns and models without oracles. In 2020 IEEE International Conference on Data Mining. IEEE, 272–281.
  78. A survey on the densest subgraph problem and its variants. arXiv preprint arXiv:2303.14467 (2023).
  79. Timothy LaRock and Renaud Lambiotte. 2023. Encapsulation Structure and Dynamics in Hypergraphs. arXiv preprint arXiv:2307.04613 (2023).
  80. Temporal locality-aware sampling for accurate triangle counting in real graph streams. The VLDB Journal 29 (2020), 1501–1525.
  81. How do hyperedges overlap in real-world hypergraphs?-patterns, measures, and generators. In Proceedings of the web conference 2021. 3396–3407.
  82. HashNWalk: Hash and Random Walk Based Anomaly Detection in Hyperedge Streams. In 31st International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence, 2129–2137.
  83. Hypergraph motifs: concepts, algorithms, and discoveries. Proceedings of the VLDB Endowment 13, 12 (2020), 2256–2269.
  84. Geon Lee and Kijung Shin. 2021. Thyme+: Temporal hypergraph motifs and fast algorithms for exact counting. In 2021 IEEE International Conference on Data Mining. IEEE, 310–319.
  85. Geon Lee and Kijung Shin. 2023. Temporal hypergraph motifs. Knowledge and Information Systems (2023), 1–38.
  86. Hypergraph Motifs and Their Extensions Beyond Binary. The VLDB Journal (2023).
  87. Graphs over time: densification laws, shrinking diameters and possible explanations. In Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining. 177–187.
  88. Graph evolution: Densification and shrinking diameters. ACM transactions on Knowledge Discovery from Data 1, 1 (2007), 2–es.
  89. Hypergraph neural networks for hypergraph matching. In Proceedings of the IEEE/CVF International Conference on Computer Vision. 1266–1275.
  90. Slashburn: Graph compression and mining beyond caveman communities. IEEE Transactions on Knowledge and Data Engineering 26, 12 (2014), 3077–3089.
  91. Hcore-init: Neural network initialization based on graph degeneracy. In 2020 25th International Conference on Pattern Recognition. IEEE, 5852–5858.
  92. Hyperbolic graph neural networks. In Proceedings of the 33rd International Conference on Neural Information Processing Systems. 8230–8241.
  93. Exact and sampling methods for mining higher-order motifs in large hypergraphs. arXiv preprint arXiv:2209.10241 (2022).
  94. Higher-order motif analysis in hypergraphs. Communications Physics 5, 1 (2022), 79.
  95. Hyperlink communities in higher-order networks. arXiv preprint arXiv:2303.01385 (2023).
  96. Learning causal effects on hypergraphs. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 1202–1212.
  97. Systematic topology analysis and generation using degree correlations. ACM SIGCOMM Computer Communication Review 36, 4 (2006), 135–146.
  98. Temporal locality and its impact on Web proxy cache performance. Performance Evaluation 42, 2-3 (2000), 187–203.
  99. The core decomposition of networks: Theory, algorithms and applications. The VLDB Journal 29 (2020), 61–92.
  100. Julian Mcauley and Jure Leskovec. 2014. Discovering social circles in ego networks. ACM Transactions on Knowledge Discovery from Data 8, 1 (2014), 1–28.
  101. Superfamilies of evolved and designed networks. Science 303, 5663 (2004), 1538–1542.
  102. Network motifs: simple building blocks of complex networks. Science 298, 5594 (2002), 824–827.
  103. Four-set Hypergraphlets for Characterization of Directed Hypergraphs. arXiv preprint arXiv:2311.14289 (2023).
  104. Introducing the graph 500. Cray Users Group 19 (2010), 45–74.
  105. Randomizing hypergraphs preserving degree correlation and local clustering. IEEE Transactions on Network Science and Engineering 9, 3 (2021), 1139–1153.
  106. Nicolas Neubauer and Klaus Obermayer. 2009. Towards community detection in k-partite k-uniform hypergraphs. In Proceedings of the NIPS 2009 Workshop on Analyzing Networks and Learning with Graphs. 1–9.
  107. Mark EJ Newman. 2001. Clustering and preferential attachment in growing networks. Physical review E 64, 2 (2001), 025102.
  108. Size-Aware Hypergraph Motifs. arXiv preprint arXiv:2311.07783 (2023).
  109. Caleb C Noble and Diane J Cook. 2003. Graph-based anomaly detection. In Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining. 631–636.
  110. Marios Papachristou and Jon Kleinberg. 2022. Core-periphery models for hypergraphs. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 1337–1347.
  111. GraphENS: Neighbor-aware ego network synthesis for class-imbalanced node classification. In International Conference on Learning Representations.
  112. Graphshap: Motif-based explanations for black-box graph classifiers. arXiv preprint arXiv:2202.08815 (2022).
  113. K-nearest neighbors in uncertain graphs. Proceedings of the VLDB Endowment 3, 1-2 (2010), 997–1008.
  114. Niels Raes and Hans ter Steege. 2007. A null-model for significance testing of presence-only species distribution models. Ecography 30, 5 (2007), 727–736.
  115. A hypergraph model for the yeast protein complex network. In 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings. IEEE, 189.
  116. Exchange pattern mining in the bitcoin transaction directed hypergraph. In Financial Cryptography and Data Security: FC 2017 International Workshops, WAHC, BITCOIN, VOTING, WTSC, and TA, Sliema, Malta, April 7, 2017, Revised Selected Papers 21. Springer, 248–263.
  117. Detecting strong ties using network motifs. In Proceedings of the 26th International Conference on World Wide Web Companion. 983–992.
  118. Community detection in large hypergraphs. Science Advances 9, 28 (2023), eadg9159.
  119. Semih Salihoglu and Jennifer Widom. 2013. Gps: A graph processing system. In Proceedings of the 25th international conference on scientific and statistical database management. 1–12.
  120. Somwrita Sarkar and Andy Dong. 2011. Community detection in graphs using singular value decomposition. Physical Review E 83, 4 (2011), 046114.
  121. Methods and metrics for cold-start recommendations. In Proceedings of the 25th annual international ACM SIGIR conference on Research and development in information retrieval. 253–260.
  122. Stephen B Seidman. 1983. Network structure and minimum degree. Social networks 5, 3 (1983), 269–287.
  123. Corescope: Graph mining using k-core analysis—patterns, anomalies and algorithms. In 2016 IEEE 16th international conference on data mining. IEEE, 469–478.
  124. Bear: Block elimination approach for random walk with restart on large graphs. In Proceedings of the 2015 ACM SIGMOD international conference on management of data. 1571–1585.
  125. Toward Degree Bias in Embedding-Based Knowledge Graph Completion. In Proceedings of the ACM Web Conference. 705–715.
  126. Georg Simmel. 1950. The sociology of georg simmel. Vol. 92892. Simon and Schuster.
  127. Konstantinos Sotiropoulos and Charalampos E Tsourakakis. 2021. Triangle-aware spectral sparsifiers and community detection. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining. 1501–1509.
  128. Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining. 1541–1551.
  129. Harnessing the power of ego network layers for link prediction in online social networks. IEEE Transactions on Computational Social Systems (2022).
  130. The why, how, and when of representations for complex systems. SIAM Rev. 63, 3 (2021), 435–485.
  131. Charalampos E Tsourakakis. 2011. Counting triangles in real-world networks using projections. Knowledge and Information Systems 26, 3 (2011), 501–520.
  132. Francesco Tudisco and Desmond J Higham. 2023. Core-periphery detection in hypergraphs. SIAM Journal on Mathematics of Data Science 5, 1 (2023), 1–21.
  133. Maria Vaida and Kevin Purcell. 2019. Hypergraph link prediction: learning drug interaction networks embeddings. In 2019 18th IEEE International Conference On Machine Learning And Applications. IEEE, 1860–1865.
  134. Distances in Higher-Order Networks and the Metric Structure of Hypergraphs. Entropy 25, 6 (2023), 923.
  135. Yanbang Wang and Jon Kleinberg. 2022. Supervised Hypergraph Reconstruction. arXiv preprint arXiv:2211.13343 (2022).
  136. Duncan J Watts and Steven H Strogatz. 1998. Collective dynamics of small-world networks. nature 393, 6684 (1998), 440–442.
  137. Douglas Brent West et al. 2001. Introduction to graph theory. Vol. 2. Prentice hall Upper Saddle River.
  138. Self-supervised hypergraph convolutional networks for session-based recommendation. In Proceedings of the AAAI conference on artificial intelligence, Vol. 35. 4503–4511.
  139. Semi-supervised hypergraph node classification on hypergraph line expansion. In Proceedings of the 31st ACM International Conference on Information & Knowledge Management. 2352–2361.
  140. Jaewon Yang and Jure Leskovec. 2012. Defining and evaluating network communities based on ground-truth. In Proceedings of the ACM SIGKDD Workshop on Mining Data Semantics. 1–8.
  141. Hypergraph partitioning for social networks based on information entropy modularity. Journal of Network and Computer Applications 86 (2017), 59–71.
  142. Sudo Yi and Deok-Sun Lee. 2022. Structure of international trade hypergraphs. Journal of Statistical Mechanics: Theory and Experiment 2022, 10 (2022), 103402.
  143. Hypergraph reconstruction from network data. Communications Physics 4, 1 (2021), 135.
  144. Zhaoning Yu and Hongyang Gao. 2022. Molecular representation learning via heterogeneous motif graph neural networks. In International Conference on Machine Learning. PMLR, 25581–25594.
  145. Testing community structure for hypergraphs. The Annals of Statistics 50, 1 (2022), 147–169.
  146. Jialiang Zhang and Jing Li. 2018. Degree-aware hybrid graph traversal on FPGA-HMC platform. In Proceedings of the 2018 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays. 229–238.
  147. Hypergraph and uncertain hypergraph representation learning theory and methods. Mathematics 10, 11 (2022), 1921.
  148. Efficiently Sampling and Estimating Hypergraphs By Hybrid Random Walk. In 2023 IEEE 39th International Conference on Data Engineering. IEEE, 1273–1285.
  149. Transfer learning of graph neural networks with ego-graph information maximization. In Advances in Neural Information Processing Systems, Vol. 34. 1766–1779.
  150. Bundle recommendation in ecommerce. In Proceedings of the 37th international ACM SIGIR conference on Research & development in information retrieval. 657–666.
Citations (6)
View on Semantic Scholar

Summary

  • The paper surveys the field of hypergraph mining, detailing patterns (static and dynamic), analytical tools and measures, and generative models for hypergraphs.
  • It highlights common patterns in real-world hypergraphs, such as heavy-tailed distributions for node degrees and hyperedge sizes, strong community structures, and temporal effects like reinforcement and densification.
  • The survey discusses various tools (e.g., motifs, decomposition) and measures (e.g., transitivity, homogeneity) for hypergraph analysis, alongside static and dynamic generative models used to replicate observed structural patterns.

Survey on Hypergraph Mining

The survey titled "A Survey on Hypergraph Mining: Patterns, Tools, and Generators" provides a comprehensive examination of hypergraphs, a robust mathematical construct for representing complex group interactions in real-world systems. Hypergraphs extend conventional graphs by allowing edges, or hyperedges, to connect any number of nodes, thus modeling polyadic relationships that cannot be accurately captured by simple dyadic connections.

Overview and Structure

The paper is structured to cover current advancements and methodologies in hypergraph mining, encompassing patterns, tools, and generators. It delineates static patterns, which apply to single-time observations, and dynamic patterns, which describe hypergraphs' temporal evolution.

Patterns: Static and Dynamic

  1. Static Patterns
    • Node-Level: Degree distributions in real-world hypergraphs are commonly heavy-tailed, implying that while many nodes have low connectivity, a few nodes serve as connectivity hubs. Hypercoreness, a centrality measure in hypergraph cores, also demonstrates this heavy-tailed characteristic.
    • Hyperedge-Level: Hyperedge size distributions follow a similar pattern, where numerous small hyperedges contrast with the occasional large hyperedge.
    • Subhypergraph-Level: High transitivity and community structures are notable, where real-world hypergraphs exhibit well-defined, densely connected community structures with high local transitivity rates.
    • Hypergraph-Level: Aggregate measures such as skewness in singular value distributions provide insights into the overall structure and hierarchy within hypergraphs.
  2. Dynamic Patterns
    • Hyperedge-Level: Temporal locality illustrates that new hyperedges are often structurally similar to recent ones, and recurring hyperedge patterns are prevalent.
    • Subhypergraph-Level: Temporal reinforcement indicates that repeated node group interactions accumulate over time, strengthening group occurrences.
    • Hypergraph-Level: Observations indicate that real-world hypergraphs undergo densification over time, with effective diameters reducing as new nodes and hyperedges enhance connectivity.

Tools and Measures

The paper highlights multiple tools and measures critical for analyzing hypergraph structures:

  • Tools: Concepts such as hypergraph motifs, temporal motifs, and multi-level decomposition help in dissecting hypergraph complexities into understandable segments.
  • Measures: Quantitative assessments, including transitivity, homogeneity, and overlapness, quantify the structural nuances of hypergraphs, contrasting them against random models to ascertain significance.

Generators for Hypergraph Modeling

Generative models are integral to reproducing observed patterns within synthetic datasets:

  • Static Generators aim to replicate distributions and structural properties observed in empirical data.
  • Dynamic Generators focus on replicating temporal evolution processes, such as preferential attachment models that mimic observed growth patterns in hypergraphs.

Implications and Future Directions

Research into hypergraph mining has significant theoretical and practical implications. Theoretically, it enhances the understanding of complex systems where polyadic interactions define system behavior. Practically, it opens avenues in diverse fields such as collaboration networks, bioinformatics, and social network analysis.

The paper proposes extending hypergraph mining into areas dealing with directed and weighted hypergraphs, emphasizing the development of efficient algorithms to leverage hypergraphs' inherently complex structures. It also suggests more applications in machine learning, noting parallels to the extensive use of graph mining techniques.

This survey acts as an essential resource, reflecting on the depth and breadth of hypergraph mining, fostering further exploration in both theoretical and applied research. The integration of hypergraphs into mainstream analysis of complex systems holds promise for unveiling intricate interaction patterns that were previously opaque to dyadic analysis.

Youtube Logo Streamline Icon: https://streamlinehq.com

YouTube