RF Hypergraphs in Satellite Communication Networks

Compelling real-world example of how RF hypergraphs are being applied to predict anomalies and optimize performance in complex systems:

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🛰️ Real-World Application: RF Hypergraphs in Satellite Communication Networks

In satellite systems—especially those involving phased array antennas and beamforming—RF hypergraphs are used to model and monitor the multi-frequency, multi-node interactions between:

• Transmitters and receivers
• Ground stations and satellites
• Frequency bands and modulation schemes

Satellite networks operate across shared RF spectra, where interference, signal degradation, or misalignment can cause:

📡 The Problem

• Loss of data integrity
• Beam misdirection
• Power inefficiencies

Traditional graph models fail to capture higher-order interference patterns, such as when three or more nodes (e.g., satellites, ground stations, and relay links) interact simultaneously across overlapping frequency bands.

🧠 The Hypergraph Solution

Researchers model the system as an RF hypergraph, where:

• Nodes = RF components (e.g., antennas, frequency bands, amplifiers)
• Hyperedges = Multi-way interactions (e.g., shared spectrum use, beamforming dependencies)

Using hypergraph neural networks (HGNNs), the system learns:

• Normal signal propagation patterns
• Expected phase and amplitude relationships
• Typical interference signatures

🚨 Anomaly Detection in Action

When a solar flare or hardware fault disrupts the RF environment:

• The hypergraph model detects nonlinear deviations in signal relationships
• It flags hyperedges with abnormal behavior (e.g., unexpected phase shifts across multiple nodes)
• Operators receive early warnings to reconfigure beam paths or adjust power levels

This approach has been used in military satellite constellations and deep-space communication arrays, where resilience and precision are critical.

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🧬 Broader Implications

This same technique is being explored in:

• Particle accelerators (like the LHC) to detect RF cavity breakdowns
• 5G/6G networks to manage dynamic spectrum allocation
• Quantum computing to model entangled qubit interactions

For a deeper dive into the structural patterns and mining tools used in real-world hypergraphs, check out the CIKM 2022 tutorial on hypergraph mining.

http://dmlab.kaist.ac.kr/~kijungs/papers/tutorialCIKM2022.pdf

Mining of Real-world Hypergraphs: Patterns, Tools, and
Generators
Geon Lee
KAIST
Seoul, South Korea
geonlee0325@kaist.ac.kr
Jaemin Yoo
Carnegie Mellon University
Pittsburgh, PA, USA
jaeminyoo@cmu.edu
Kijung Shin
KAIST
Seoul, South Korea
kijungs@kaist.ac.kr
ABSTRACT
Group interactions are prevalent in various complex systems (e.g.,
collaborations of researchers and group discussions on online Q&A
sites), and they are commonly modeled as hypergraphs. Hyperedges, which compose a hypergraph, are non-empty subsets of any
number of nodes, and thus each hyperedge naturally represents
a group interaction among entities. The higher-order nature of
hypergraphs brings about unique structural properties that have
not been considered in ordinary pairwise graphs.
In this tutorial, we offer a comprehensive overview of a new
research topic called hypergraph mining. We first present recently
revealed structural properties of real-world hypergraphs, including
(a) static and dynamic patterns, (b) global and local patterns, and (c)
connectivity and overlapping patterns. Together with the patterns,
we describe advanced data mining tools used for their discovery.
Lastly, we introduce simple yet realistic hypergraph generative
models that provide an explanation of the structural properties.
CCS CONCEPTS

• Information systems → Social networks; Data mining.
  KEYWORDS
  hypergraphs, social networks, structure mining, graph generators
  ACM Reference Format:
  Geon Lee, Jaemin Yoo, and Kijung Shin. 2022. Mining of Real-world Hypergraphs: Patterns, Tools, and Generators. In Proceedings of the 31st ACM
  International Conference on Information and Knowledge Management (CIKM
  ’22), October 17–21, 2022, Atlanta, GA, USA. ACM, New York, NY, USA,
  4 pages. https://doi.org/10.1145/3511808.3557505
  1 BASIC INFORMATION
• The tutorial is half-day long, i.e., 3 hours with breaks.
• The slides for this tutorial are available at https://sites.google.
  com/view/hypergraph-tutorial-cikm.
  Permission to make digital or hard copies of all or part of this work for personal or
  classroom use is granted without fee provided that copies are not made or distributed
  for profit or commercial advantage and that copies bear this notice and the full citation
  on the first page. Copyrights for components of this work owned by others than ACM
  must be honored. Abstracting with credit is permitted. To copy otherwise, or republish,
  to post on servers or to redistribute to lists, requires prior specific permission and/or a
  fee. Request permissions from permissions@acm.org.
  CIKM ’22, October 17–21, 2022, Atlanta, GA, USA
  © 2022 Association for Computing Machinery.
  ACM ISBN 978-1-4503-9236-5/22/10. . . $15.00
  https://doi.org/10.1145/3511808.3557505
  Figure 1: The co-authorship among five authors in four publications [7, 19–21] are represented as a hypergraph with five
  nodes and four hyperedges.
  2 IMPORTANCE AND RELEVANCE
  Group interactions are omnipresent in real-world complex systems:
  collaborations of researchers, joint interactions of proteins, copurchases of items, to name a few. Such group interactions among
  entities are commonly modeled as a hypergraph, which consists of
  nodes and hyperedges (see Figure 1 for an example). A hyperedge,
  which is a non-empty subset of nodes, naturally models a group
  interaction among any number of entities. Thanks to the powerful
  expressiveness of hypergraphs, they have been used in a wide
  range of fields, including recommender systems [22, 30], computer
  vision [17, 27], natural language processing [9, 12], social network
  analysis [28], bioinformatics [14], and circuit designs [16].
  Motivated by the successful investigation of structural patterns
  in real-world pairwise graphs (e.g., power-law degree distribution [1, 11], six degrees of separation [13, 15], and network motifs [24, 25]) and their wide range of applications, such patterns in
  real-world hypergraphs have been extensively studied recently. The
  flexibility in the size of each hyperedge, which provides the expressiveness of hypergraphs, brings about unique structural properties
  that have not been considered in pairwise graphs, and specialized
  tools have been developed to analyze their structural patterns. Moreover, several efforts have been made to reproduce and thus explain
  the patterns through intuitive hypergraph generative models.
  In this half-day tutorial, we provide a comprehensive overview of
  structural patterns discovered in real-world hypergraphs, advanced
  data mining tools for hypergraphs, and hypergraph generative
  models based on the patterns.
  While this topic hypergraph mining is in its infant stage, we
  believe it will be of interest of a much larger group of researchers,
  CIKM ’22, October 17–21, 2022, Atlanta, GA, USA Geon Lee, Jaemin Yoo, & Kijung Shin
• Part I: Introduction
  ◦ Group interactions in the real-world
  ◦ Power of hypergraph modeling [26, 29]
  ◦ Data repositories and open-source software for hypergraph mining
• Part II: Static Structural Patterns in Hypergraphs and Data Mining Tools for Their Discovery
  ◦ Basic patterns
  ⋄ Node-level properties [10, 18, 19]
  ⋄ Hyperedge-level properties [18, 19]
  ⋄ Hypergraph-level properties [2, 10, 18]
  ◦ Advanced patterns (sub-hypergraph-level properties) [2, 19, 20, 23]
• Part III: Dynamic Structural Patterns in Hypergraphs and Data Mining Tools for Their Discovery
  ◦ Basic patterns
  ⋄ Node-level properties [3, 7]
  ⋄ Hyperedge-level properties [3, 4, 21]
  ⋄ Hypergraph-level properties [18]
  ◦ Advanced patterns (sub-hypergraph-level properties) [2, 8, 21]
• Part IV: Generative Models of Hypergraphs
  ◦ Full-hypergraph generation
  ⋄ Static hypergraphs [5, 19]
  ⋄ Dynamic hypergraphs [10, 18]
  ◦ Sub-hypergraph generation
  ⋄ Static sub-hypergraphs [6]
  ⋄ Dynamic sub-hypergraphs [3, 8]
  Figure 2: The brief outline of the proposed tutorial.
  especially those interested in graphs, when considering the representational power, usability, and omnipresence of hypergraphs.
  Moreover, patterns and generative models of hypergraph data will
  have a huge impact on our understanding of complex systems and
  also on various applications, including algorithm design, simulation, and anomaly detection, as those of graph data do. This tutorial
  aims to provide a starting point for further studies on this topic.
  Relevance to CIKM: This tutorial on novel and interdisciplinary
  directions covers various aspects of data mining, including findings,
  algorithms, and applications. It should be noticed that more than
  half of the studies covered in the tutorial appeared in conferences
  in data mining (specifically, ICDM, KDD, WWW, VLDB, and SDM).
  3 TARGET AUDIENCE AND PREREQUISITES
  This tutorial is targeted at anyone interested in graph mining,
  graph learning, social network analysis, or network science, from
  researchers to the practitioners from industry. It should be noticed
  that hypergraphs have been used for modeling data from a variety
  of domains, including recommender systems [22, 30], computer
  vision [17, 27], natural language processing [9, 12], social network
  analysis [28], and thus they are of interest to practitioners.
  Basic knowledge of linear algebra and probability theory will
  be helpful. For the audience new to this field, we will cover all
  necessary preliminaries and provide an intuitive overview of recent
  studies on the topic. We will also offer in-depth descriptions of
  advanced techniques for the audience with more experience in
  this field. Specifically, the audience of this tutorial will be able
  to (1) understand the basic hypergraph-related concepts, (2) use
  the concepts to model and analyze group interactions in various
  real-world complex systems, and (3) understand structural design
  principles of real-world hypergraphs.
  4 OUTLINE AND CONTENTS
  We provide a brief outline of the tutorial in Figure 2.
  In this tutorial, we focus on providing a comprehensive overview
  of structural patterns discovered in real-world hypergraphs, and
  advanced data mining tools for large-scale hypergraphs. As an introduction, we present how hypergraphs are used to model various
  types of data from different domains.
  During the first half of this tutorial, we introduce structural patterns pervasive in real-world hypergraphs. Specifically, we cover (a)
  static structural patterns1
  [2, 10, 18–20, 23] and (b) dynamic structural patterns2
  [2, 3, 7, 8, 18, 21] of real-world hypergraphs where
  the static patterns are further divided into (a) node-level patterns,
  (b) hyperedge-level patterns, (c) sub-hypergraph-level patterns, and
  (d) hypergraph-level patterns, as summarized in Table 1. The presented patterns include macroscopic (i.e., global) [10, 18, 19] and
  microscopic (i.e., local) [2, 20, 21, 23] patterns, and they also include
  patterns regarding connectivity [10, 18, 23], overlap [2, 8, 19–21],
  and repetition [3, 4, 7] of hyperedges. Together with the patterns,
  we present advanced data mining tools (e.g., hypergraph motifs
  [20, 21], multi-level decomposition [10], and a principled measure
  of “overlapness” [19]) developed for their discovery.
  During the second half, we present generative models of hypergraphs, which are based on the observations made in real-world
  hypergraphs. They aim to reproduce and thus explain the structural patterns through intuitive mechanisms on individual nodes or
  hyperedges. These models can also be used for creating large-scale
  benchmark datasets, for anonymizing hypergraphs with sensitive
  information, and for comparing hypergraphs of different sizes. As
  categorized in Table 2, we cover four models for generating entire
  1Patterns from static hypergraphs or a few snapshots.
  2Patterns related to the dynamics of evolving hypergraphs.
  Mining of Real-world Hypergraphs: Patterns, Tools, and Generators CIKM ’22, October 17–21, 2022, Atlanta, GA, USA
  Table 1: Categorization of structural properties in real-world hypergraphs that are covered in this tutorial.
  Static patterns* (Part II) Dynamic patterns** (Part III)
  Nodes Hyperedges Sub-hypergraphs Hypergraphs Nodes Hyperedges Sub-hypergraphs Hypergraphs
  Benson et al. (PNAS’18) [2] ✓ ✓ ✓
  Benson et al. (KDD’18) [3] ✓ ✓
  Cencetti et al. (SciRep’21) [4] ✓
  Choo and Shin (SDM’22) [7] ✓
  Comrie and Kleinberg (ICDM’21) [8] ✓
  Do et al. (KDD’20) [10] ✓ ✓
  Kook et al. (ICDM’20) [18] ✓ ✓ ✓ ✓
  Lee et al. (WWW’21) [19] ✓ ✓ ✓
  Lee et al. (VLDB’20) [20] ✓
  Lee and Shin (ICDM’21) [21] ✓ ✓
  Lotito et al (CommsPhys’22) [23] ✓
  *Patterns from static hypergraphs or a few snapshots. **Patterns related to the dynamics of evolving hypergraphs.
  Table 2: Comparison of the hypergraph generative models
  covered in this tutorial.
  Full hypergraphs Sub-hypergraphs
  Static Dynamic Static Dynamic
  Benson et al. (KDD’18) [3] ✓
  Comrie and Kleinberg (ICDM’21) [8] ✓
  Chodrow (J. Complex Netw’20) [5] ✓
  Choe et al (WWW’22) [6] ✓
  Do et al. (KDD’20) [10] ✓
  Kook et al. (ICDM’20) [18] ✓
  Lee et al. (WWW’21) [19] ✓
  hypergraphs models [5, 10, 18, 19] and two models for generating
  sub-hypergraphs [3, 6, 8]. In addition to their technical details, we
  present how realistic they are in various aspects.
  5 IMPORTANT REFERENCES
  The important references covered in the tutorial are provided below.
• [PNAS’18] Austin R Benson, Rediet Abebe, Michael T Schaub, Ali
  Jadbabaie, and Jon Kleinberg. Simplicial closure and higher-order
  link prediction. PNAS, 115(48):E11221–E11230, 2018.
• [KDD’18] Austin R Benson, Ravi Kumar, and Andrew Tomkins.
  Sequences of sets. In KDD, 2018
• [SciRep’21] Giulia Cencetti, Federico Battiston, Bruno Lepri, and
  Márton Karsai. Temporal properties of higher-order interactions in
  social networks. Scientific reports, 11(1):1–10, 2021.
• [J. Complex Netw’20] Philip S Chodrow. Configuration models of
  random hypergraphs. J. Complex Networks, 8(3):cnaa018, 2020.
• [WWW’22] Minyoung Choe, Jaemin Yoo, Geon Lee, Woonsung
  Baek, U Kang, and Kijung Shin. Midas: Representative sampling
  from real-world hypergraphs. In WWW, 2022.
• [SDM’22] Hyunjin Choo and Kijung Shin. On the persistence of
  higher-order interactions in real-world hypergraphs. SDM, 2022.
• [ICDM’21a] Cazamere Comrie and Jon Kleinberg. Hypergraph
  ego-networks and their temporal evolution. In ICDM, 2021.
• [KDD’20] Manh Tuan Do, Se-eun Yoon, Bryan Hooi, and Kijung Shin. Structural patterns and generative models of real-world
  hypergraphs. In KDD, 2020.
• [ICDM’20] Yunbum Kook, Jihoon Ko, and Kijung Shin. Evolution
  of real-world hypergraphs: Patterns and models without oracles. In
  ICDM, 2020.
• [WWW’21] Geon Lee, Minyoung Choe, and Kijung Shin. How do
  hyperedges overlap in real-world hypergraphs?-patterns, measures,
  and generators. In WWW, 2021.
• [VLDB’20] Geon Lee, Jihoon Ko, and Kijung Shin. Hypergraph motifs: concepts, algorithms, and discoveries. PVLDB, 13(12):2256–2269,
  2020.
• [ICDM’21b] Geon Lee and Kijung Shin. THyMe+: Temporal hypergraph motifs and fast algorithms for exact counting. In ICDM,
  2021.
• [CommPhys’22] Quintino Francesco Lotito, Federico Musciotto,
  Alberto Montresor, and Federico Battiston. Higher-order motif
  analysis in hypergraphs. Comm. Phys, 5(1):1–8, 2022.
• [SIREV’21] Leo Torres, Ann S. Blevins, Danielle Bassett, and Tina
  Eliassi-Rad. The why, how, and when of representations for complex
  systems. SIAM Review 63(3):435-485, 2021
  6 RELEVANT TUTORIALS
  There have been tutorials on mining of graphs in general, including:
• Graph Structures in Data Mining in KDD 2004
  – http://www.cs.cmu.edu/~christos/TALKS/KDD04-tut/
  – This tutorial focuses on (1) topological properties of nodes and
  edges, (2) importance measures of nodes, and (3) similarity and
  influence between nodes in graphs.
• Large Graph Mining: Patterns, Tools, and Case Studies in CIKM
  2008 & ICDE 2009
  – http://tonghanghang.org/pdfs/tut-icde09-part1_patterns.pdf
  – This tutorial focuses on (1) structural patterns, (2) matrix &
  tensor tools, (3) proximity measures between nodes, and (4)
  case studies of real-world graphs.
• Mining Billion-Scale Graphs: Patterns and Algorithms in SIGMOD
  2012
  – https://www.cs.cmu.edu/~christos/TALKS/12-SIGMOD-tutorial/
  – This tutorial focuses on (1) patterns in real-world graphs, (2)
  tools for pattern mining in graphs, and (3) scalable algorithms
  for large-scale graphs.
• Advanced Graph Mining for Community Evaluation in Social Networks and the Web in WSDM 2013
  – http://www.lix.polytechnique.fr/~mvazirg/WSDM2013_tutorial
  – This tutorial focuses on detection and evaluation methods of
  communities in graphs.
• Big Graph Mining: Algorithms, Anomaly Detection, and Applications in ASONAM 2013
  CIKM ’22, October 17–21, 2022, Atlanta, GA, USA Geon Lee, Jaemin Yoo, & Kijung Shin
  – https://datalab.snu.ac.kr/~ukang/talks/13-ASONAM-tutorial/
  – This tutorial focuses on (1) scalable graph mining, (2) graphbased anomaly detection, and (3) applications.
• Core Decomposition of Networks: Concepts, Algorithms and Applications in ICDM 2016 & PKDD 2017
  – https://fragkiskos.me/projects/core_tutorial/
  – This tutorial focuses on (a) the concept and properties of core
  decomposition, (b) efficient computation, and (c) applications.
• Roles in Networks – Foundations, Methods and Applications in
  ICDM 2021
  – https://cswzhang.github.io/icdm-tutorial-2021/
  – This tutorial focuses on (a) the taxonomy of role analytic methods, (b) role-based embedding methods, (c) and applications.
  To the best of our knowledge, however, no tutorial that focuses on
  hypergraphs has been offered in data-mining and related venues.
  The patterns, tools and models covered in this tutorial are clearly
  distinguished from those for ordinary graphs. We plan to deliver
  the same tutorial at DSAA 2022 and ICDM 2022.
  7 SHORT BIO OF PRESENTERS
  Geon Lee (https://geonlee0325.github.io) is a Ph.D. student at the
  Kim Jaechul Graduate School of AI at KAIST. He received his B.S.
  degree in Computer Science and Engineering from Sungkyunkwan
  University in 2019. His research interests include graph mining
  and its applications. Especially, his studies of hypergraphs have
  appeared in major data mining venues, including VLDB, WWW,
  and ICDM.
  Jaemin Yoo (https://jaeminyoo.github.io) is a postdoctoral research
  fellow in the Heinz College of Information Systems and Public
  Policy at Carnegie Mellon University. He received his Ph.D. and
  B.S. in Computer Science and Engineering from Seoul National
  University. His research interests include probabilistic mining and
  machine learning on graphs. His work has been published in major
  venues including WWW, KDD, and NeurIPS. He is a recipient of the
  Google PhD Fellowship and the Qualcomm Innovation Fellowship.
  Kijung Shin (https://kijungs.github.io/) is an Ewon Endowed Assistant Professor (jointly affiliated) in the Kim Jaechul Graduate
  School of AI and the School of Electrical Engineering at KAIST.
  He received his Ph.D. in Computer Science from Carnegie Mellon
  University in 2019. He has published more than 50 referred articles
  at major data mining venues, and he won the best research paper
  award at KDD 2016. His research interests span a wide range of
  topics on graph mining, with a focus on scalable algorithm design
  and empirical analysis of real-world hypergraphs.
  ACKNOWLEDGEMENTS
  This work was supported by National Research Foundation of Korea
  (NRF) grant funded by the Korea government (MSIT) (No. NRF2020R1C1C1008296) and Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the
  Korea government (MSIT) (No. 2022-0-00157, Robust, Fair, Extensible Data-Centric Continual Learning).
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