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How Do Hyperedges Overlap in Real-World Hypergraphs? – Patterns, Measures, and Generators [article]

Geon Lee, Minyoung Choe, Kijung Shin
2021 arXiv   pre-print
To this end, we define principled measures and statistically compare the overlaps of hyperedges in real-world hypergraphs and those in null models.  ...  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  ...  This unique property of hypergraphs poses important questions that have not been considered in graphs: (1) How do hyperedges overlap in real-world hypergraphs?  ... 
arXiv:2101.07480v4 fatcat:hofpunybingtfiipibcxhjjbjy

Hypergraph Simultaneous Generators

Bahman Pedrood, Carlotta Domeniconi, Kathryn B. Laskey
2022 International Conference on Artificial Intelligence and Statistics  
While the models designed for hypergraphs attempt to capture the latter, they add further strict assumptions on the structure and size of hyperedges and are usually computationally intractable for real  ...  This paper proposes an efficient probabilistic generative model for detecting overlapping communities that process hyperedges without any changes or restrictions on their size.  ...  truth in real- world networks.  ... 
dblp:conf/aistats/PedroodDL22 fatcat:bavjh4inpbho5eqehemmetist4

Evolution of Real-world Hypergraphs: Patterns and Models without Oracles [article]

Yunbum Kook, Jihoon Ko, Kijung Shin
2020 arXiv   pre-print
What kind of macroscopic structural and dynamical patterns can we observe in real-world hypergraphs?  ...  In this work, we closely examine seven structural and dynamical properties of real hypergraphs from six domains.  ...  INTRODUCTION Which structural patterns do real-world hypergraphs have and how do they evolve over time? Are there simple mechanisms on individual nodes that these patterns emerge from?  ... 
arXiv:2008.12729v2 fatcat:m32bkwzucfdppclh4a5sngjrbm

Hypergraph Motifs: Concepts, Algorithms, and Discoveries [article]

Geon Lee, Jihoon Ko, Kijung Shin
2020 arXiv   pre-print
In this work, we propose tools for answering the following questions in a systematic manner: (Q1) what are structural design principles of real-world hypergraphs?  ...  In addition, we demonstrate that CPs capture local structural patterns unique in each domain, and thus comparing CPs of hypergraphs addresses Q2 and Q3.  ...  The successful investigation and discovery of local structural patterns in real-world graphs motivates us to explore local structural patterns in real-world hypergraphs.  ... 
arXiv:2003.01853v1 fatcat:xtol4x4zszb2bdwrmkh2cxl4ra

On the Persistence of Higher-Order Interactions in Real-World Hypergraphs [article]

Hyunjin Choo, Kijung Shin
2022 arXiv   pre-print
Our focus is the persistence of HOIs repeated over time, which is naturally interpreted as the strength of group relationships, aiming at answering three questions: (a) How do HOIs in real-world hypergraphs  ...  First, we define how to measure the persistence of HOIs. Then, we examine global patterns and anomalies in the persistence, revealing a power-law relationship.  ...  The significance of the persistence of HOIs brings up important questions that have not been answered yet: (a) How do higher-order interactions in real-world hypergraphs persist over time?  ... 
arXiv:2201.00972v2 fatcat:yoywhd2h3fc55hczgzcg5roohe

Semantic Graph Compression with Hypergraphs

Arber Borici, Alex Thomo
2014 2014 IEEE 28th International Conference on Advanced Information Networking and Applications  
We provide empirical results that compare the proposed method to random and natural orderings of select real networks using an information-theoretic measure.  ...  In this paper, we propose a modeling and compression technique that consists of two phases: (i) mapping networks to hypergraphs by exploiting inherent or structural semantic features; and (ii) partitioning  ...  a real-world graph.  ... 
doi:10.1109/aina.2014.133 dblp:conf/aina/BoriciT14 fatcat:4cgmyxxnsjhzzab2lkx4oqpesm

Higher-order motif analysis in hypergraphs [article]

Quintino Francesco Lotito, Federico Musciotto, Alberto Montresor, Federico Battiston
2021 arXiv   pre-print
We identify different families of hypergraphs, characterized by distinct higher-order connectivity patterns at the local scale.  ...  Our work highlights the informative power of higher-order motifs, providing a first way to extract higher-order fingerprints in hypergraphs at the network microscale.  ...  relevance of the higher-order nature of interactions in many real-world systems.  ... 
arXiv:2108.03192v1 fatcat:q74km7myhng3xhs3qhogsi7ppa

Principled inference of hyperedges and overlapping communities in hypergraphs [article]

Martina Contisciani, Federico Battiston, Caterina De Bacco
2022 arXiv   pre-print
The method allows to infer missing hyperedges of any size in a principled way, and to jointly detect overlapping communities in presence of higher-order interactions.  ...  We apply our method to a variety of real-world systems, showing strong performance in hyperedge prediction tasks, detecting communities well aligned with the information carried by interactions, and robustness  ...  real-world hypergraphs.  ... 
arXiv:2204.05646v1 fatcat:7eme55htvnh4pfcdsdl5evijge

Detecting Topic-oriented Overlapping Community Using Hybrid Hypergraph Model

Gui-lan Shen, Xiao-ping Yang, Jie Sun
2016 International Journal of Computers Communications & Control  
A novel hyperedge pair similarity measure is proposed by combining linearly extended common neighbors metric for real connection and incremental fitness for virtual connection.  ...  Two connections for hyperedge pair, including real connection and virtual connection are defined.  ...  In real-world network, it's difficult to decide how many communities that a single node should be put in, however it's very clear whether the edge incident on the node is in the community or not.  ... 
doi:10.15837/ijccc.2016.4.2166 fatcat:3cn5urammzcx7mbdvgnzqbcnuq

MESH: A Flexible Distributed Hypergraph Processing System [article]

Benjamin Heintz, Rankyung Hong, Shivangi Singh, Gaurav Khandelwal, Corey Tesdahl, Abhishek Chandra
2019 arXiv   pre-print
Research has shown that such group dynamics can be better modeled through a more general hypergraph model, resulting in the need to build scalable hypergraph processing systems.  ...  Using a variety of real datasets and experiments conducted on a local 8-node cluster as well as a 65-node Amazon AWS testbed, we demonstrate that MESH provides flexibility based on data and application  ...  ACKNOWLEDGMENTS This work is supported in part by NSF grant III-1422802.  ... 
arXiv:1904.00549v2 fatcat:lgfgdpjnvjecxnwcrsm35pexpa

HYPE: Massive Hypergraph Partitioning with Neighborhood Expansion [article]

Christian Mayer and Ruben Mayer and Sukanya Bhowmik and Lukas Epple and Kurt Rothermel
2018 arXiv   pre-print
Many important real-world applications-such as social networks or distributed data bases-can be modeled as hypergraphs.  ...  In such a model, vertices represent entities-such as users or data records-whereas hyperedges model a group membership of the vertices-such as the authorship in a specific topic or the membership of a  ...  and it holds for real-world hypergraphs as well.  ... 
arXiv:1810.11319v4 fatcat:dvq4c47myvefzhgd3glgfqoqtq

Exact and Sampling Methods for Mining Higher-Order Motifs in Large Hypergraphs [article]

Quintino Francesco Lotito, Federico Musciotto, Federico Battiston, Alberto Montresor
2022 arXiv   pre-print
In this work, we focus on the problem of counting occurrences of sub-hypergraph patterns in very large higher-order networks.  ...  They highlight fundamental aspects of the interplay between the topology and the dynamics of complex networks and have a wide range of real-world applications.  ...  Lee et al. characterize real-world hypergraphs at their microscale in terms of patterns of connected hyperedges of fixed size [23] .  ... 
arXiv:2209.10241v1 fatcat:3oduahulkzdvbjjyifo7ocgtbm

Entropy-based random models for hypergraphs [article]

Fabio Saracco, Giovanni Petri, Renaud Lambiotte, Tiziano Squartini
2022 arXiv   pre-print
Here, we propose null models to analyse hypergraphs that generalise the classical Erd\"os-R\'enyi and Configuration Model by randomising incidence matrices in a constrained fashion.  ...  After discussing them, we extend the definition of several network quantities to hypergraphs, derive their expected values and compare them with empirical ones, to detect significant deviations from random  ...  EP/V013068/1 and EP/V03474X/1. TS acknowledges support from the EU H2020 project 'SoBigData++', grant n. 871042.  ... 
arXiv:2207.12123v1 fatcat:d6uojdicfbc4fbqhal5klybajq

Hypergraph Partitioning With Embeddings [article]

Justin Sybrandt, Ruslan Shaydulin, Ilya Safro
2020 arXiv   pre-print
A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect any number of nodes. As a result, hypergraph partitioning is an NP-Hard problem to both solve or approximate.  ...  In this work we propose using graph embeddings of the initial hypergraph in order to ensure that coarsened problem instances retrain key structural features.  ...  We would also like to thank our editor and reviewers.  ... 
arXiv:1909.04016v5 fatcat:wfpycc6sirdsnasocgyp72375a

MESH: A Flexible Distributed Hypergraph Processing System

Benjamin Heintz, Rankyung Hong, Shivangi Singh, Gaurav Khandelwal, Corey Tesdahl, Abhishek Chandra
2019 2019 IEEE International Conference on Cloud Engineering (IC2E)  
Research has shown that such group dynamics can be better modeled through a more general hypergraph model, resulting in the need to build scalable hypergraph processing systems.  ...  Using a variety of real datasets, we experimentally demonstrate that MESH provides flexibility based on data and application characteristics, examine its scaling with cluster size, and show that it is  ...  Scalability: Many real-world datasets range in size from small to massive, comprising millions or billions of vertices and hyperedges.  ... 
doi:10.1109/ic2e.2019.00-11 dblp:conf/ic2e/HeintzHSKTC19 fatcat:wm5acuzafjdn5kvbvaqtkttviq
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