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About 9,705 papers for “Hypergraph”

Hypergraph convolution and hypergraph attention

Song Bai, Feihu Zhang, Philip H. S. Torr · Pattern Recognition · 2020

Cited by 709

Hypergraph Transversals

Georg Gottlob · Lecture notes in computer science · 2004

Cited by 6

Hypergraph Versals

Vance Faber, Noah Streib · arXiv (Cornell University) · 2016

Let H be a hypergraph on n vertices with the property that no edge contains another. We prove some results for a special case of the Isolation Lemma when the label set for the edges of H can only take two values. Given any set of vertices S and an edge e, the weight of S in e is the size of e plus the size of the intersection of S and e. A versal S for an edge e is a set of vertices with weight in e smaller than the weight in any other edge. We show that H always has at least n + 1 versals except if H is either the set of all singletons T_n or the complement of T_n or the 4-cycle graph. In those exceptional cases there are only n versals.

Cited by 0Open access

Autoregressive hypergraph

Xianghe Zhu, Qiwei Yao · London School of Economics and Political Science Research Online (London School of Economics and Political Science) · 2026

Traditional graph representations are insufficient for modelling real-world phenom ena involving multi-entity interactions, such as collaborative projects or protein complexes, necessitating the use of hypergraphs. While hypergraphs preserve the intrinsic nature of such complex relationships, existing models often overlook tem poral evolution in relational data. To address this, we introduce a first-order autore gressive (i.e. AR(1)) model for dynamic non-uniform hypergraphs. This is the first dynamic hypergraph model with provable theoretical guarantees, explicitly defining the temporal evolution of hyperedge presence through transition probabilities that govern persistence and change dynamics. This framework provides closed-form ex pressions for key probabilistic properties and facilitates straightforward maximum likelihood inference with uniform error bounds and asymptotic normality, along with a permutation-based diagnostic test. We also consider an AR(1) hypergraph stochastic block model (HSBM), where a novel Laplacian enables exact and effi cient latent community recovery via a spectral clustering algorithm. Furthermore, we develop a likelihood-based change-point estimator for the HSBM to detect struc tural breaks. The efficacy and practical value of our methods are comprehensively demonstrated through extensive simulation studies and compelling applications to a primary school interaction data set and the Enron email corpus, revealing insightful community structures and significant temporal changes.

Cited by 0

Hypergraph Rewriting:

Critical Pairs And, Undecidability Of Confluence, Detlef Plump · 2007

this paper is the completion of non-confluent systems. One could set up a procedure which adds rules to a system until all critical pairs are strongly joinable, where the new rules should preserve the equivalence , generated by ). The hypergraph rewriting systems submitted to such a procedure would have to be terminating, to ensure that strong joinability can be checked. This poses the question of how to test for termination of (hyper)graph rewriting systems, a topic to which apparently very little attention has been paid yet

Cited by 0

Hypergraph NIM

Mursic, Peter · Rutgers University Community Repository (Rutgers University) · 2019

NIM is a game in which two players take turns removing tokens from piles. There are usually several non overlapping piles each of which can have any amount of tokens in it. In a turn a player selects a nonempty pile and removes any positive number of tokens from it. The player that removed the last token(s) wins the game.This thesis focused on a generalization of the game NIM in which players on their turn instead of selecting a particular pile, they select a subset of piles and then proceed to remove and positive amount of tokens from each pile i.e. at least on token from each pile. Not all subsets of piles can be selected though, the available options are usually given as a hypergraph H. Also if any of the piles are empty then the corresponding moves that include that pile are no longer legal. If not specifically said otherwise we assume the base set of H is V i.e. H ⊆ 2V This generalization we named Hypergraph NIM and it is a very broad generalization as it also includes other NIM generalizations like Moore’s NIM [25].

Cited by 0Open access

Hypergraph Partitioning

Ümit V. Çatalyürek, Bora Uçar, Cevdet Aykanat · HAL (Le Centre pour la Communication Scientifique Directe) · 2011

Cited by 1Open access

Hypergraph v0.10.7

Liberate Science · 2021

We just released Hypergraph (Beta) v0.10.7 [https://libscie.org/hypergraph]. An announcement is coming on September 10th that will affect the future release schedule. If you have Hypergraph (Beta) installed, it will auto-install next time you run it. Below, you can find a detailed and human-readable version of what we changed.

Cited by 0Open access

Hypergraph v0.10.5

Liberate Science · 2021

We just released Hypergraph (Beta) v0.10.5 [https://hypergraph.xyz] 🎉 New releases of Hypergraph occur on the 28th of every month — we only break that cycle if there are urgent fixes that we need to ship as soon as possible (e.g., for security). If you're interested in understanding how we version our releases, check out Semantic Versioning [https://semver.org/]. If you have Hypergraph (Beta) installed, it will auto-install next time you run it

Cited by 0Open access

Hypergraph Categories

Brendan Fong, David I. Spivak · arXiv (Cornell University) · 2018

Hypergraph categories have been rediscovered at least five times, under various names, including well-supported compact closed categories, dgs-monoidal categories, and dungeon categories. Perhaps the reason they keep being reinvented is two-fold: there are many applications---including to automata, databases, circuits, linear relations, graph rewriting, and belief propagation---and yet the standard definition is so involved and ornate as to be difficult to find in the literature. Indeed, a hypergraph category is, roughly speaking, a "symmetric monoidal category in which each object is equipped with the structure of a special commutative Frobenius monoid, satisfying certain coherence conditions". Fortunately, this description can be simplified a great deal: a hypergraph category is simply a "cospan-algebra". The goal of this paper is to remove the scare-quotes and make the previous statement precise. We prove two main theorems. First is a coherence theorem for hypergraph categories, which says that every hypergraph category is equivalent to an objectwise-free hypergraph category. Second, we prove that the category of objectwise-free hypergraph categories is equivalent to the category of cospan-algebras.

Cited by 2Open access

Hypergraph Modeling

Qionghai Dai, Yue Gao · Artificial intelligence: foundations, theory, and algorithms/Artificial intelligence: Foundations, theory, and algorithms · 2023

Abstract Hypergraph modeling is the fundamental task in hypergraph computation, which targets on establishing a high-quality hypergraph structure to accurately formulate the high-order correlation among data. In this section, we introduce different hypergraph modeling methods to show how to build hypergraphs using various pieces of information, such as features, attributes, and/or graphs. These methods are organized into two broad categories, depending on whether these correlations are explicit or implicit, to distinguish the similarities and differences. We then further discuss different hypergraph structure optimization and generation methods, such as adaptive hypergraph modeling, generative hypergraph modeling, and knowledge hypergraph generation.

Cited by 1Open access

Hypergraph Computation

Qionghai Dai, Yue Gao · Artificial intelligence: foundations, theory, and algorithms/Artificial intelligence: Foundations, theory, and algorithms · 2023

This open access book objective is to explore the theory and methods of hypergraph computation and summarize its recent achievements and future directions.

Cited by 27Open access

Imports hypergraph

K. Gavai, Hannes Hettling, Maintainer Anand K. Gavai et al. · 2014

Cited by 0

Hypergraph Codes

Yonatan Bilu, Shlomo Hoory · 2001

We propose a new family of asymptotically good binary codes, generalizing previous constructions of expander codes to t-uniform hypergraphs. These new codes have a better distancerate tradeoff than that known for expander codes. For high rates they also improve the known results for decoding distance. Our construction starts from a small code C 0 f0; 1g , with relative distance 0 and rate r 0 , and a family of expanding t-uniform t-partite -regular hypergraphs. Our code has rate tr 0 (t 1), and relative distance t t 1 0 o(1). When t = 2l + 1 we also suggest a decoding algorithm, and prove it decodes correctly up to a 2l+1 l 1 l 0 2 (l+1)=l o(1) fraction of errors. (The o(1) term refers to the growing of the hyperegraph).

Cited by 0

Hypergraph datasets

He, Yichen · Figshare · 2025

# Hypergraph Dataset### spec- Star War IV New Hope actor collaberation network - `star-war-adjMat.csv`: node-hyperedge adjacency matrix - `star-war-actor-lst.csv`: main charactors' names - `star-war-feat-hat.Rdata`: estimated latent covariate returned by MCEM - AOS coauthorship network feb issue in 2021 - `aos-feb-adjMat.csv`: node-hyperedge adjacency matrix - `aos-feb-author-lst.csv`: authors' real names - `aos-feb-feat-hat.Rdata`: estimated latent covariate returned by MCEM - AOS coauthorship network 2021 four issures: feb, apr, jun, aug - `aos-yearly-adjMat.csv`: node-hyperedge adjacency matrix - `aos-yearly-author-lst.csv`: authors' real names

Cited by 0Open access

Hypergraph construction.

Elizabeth N. Davison (682496), Benjamin O. Turner (3360653), Kimberly J. Schlesinger (603200) et al. · Figshare · 2016

An illustration of hyperedge identification on a representational set of edges. Edge weights are computed separately for each time window (A) and joined together to form edge weight time series (B). Significantly correlated edge time series are cross-linked to form a hyperedge, a group of nodes that are linked by correlated edges (C). The group of hyperedges for an individual, with singletons removed, forms a hypergraph (D).

Cited by 0Open access

Hypergraph burning

Jones, Caleb · Memorial University Research Repository (Memorial University) · 2023

Graph burning is a combinatorial game or process that models the spread of in\nuence\nthroughout a network. We introduce a generalization of graph burning which applies to\nhypergraphs. One of our key results is that arbitrary hypergraphs do not satisfy a bound\nanalogous to the one in the Burning Number Conjecture. We also introduce a variant called\n\\lazy" hypergraph burning, along with a new parameter, the lazy burning number. Interestingly,\nlazily burning a graph is trivial, while lazily burning a hypergraph can be quite\ncomplicated. Moreover, the lazy burning model is a useful tool for analyzing the roundbased\nmodel. We obtain bounds on the burning number and lazy burning number of a\nhypergraph in terms of its parameters, as well as stronger bounds that apply to Steiner\ntriple systems. We also discuss the complexity of both the round-based and lazy models.\nFinally, we introduce two further variants of (lazy) hypergraph burning.

Cited by 0Open access

Hypergraph Partitioning

Cédric Chevalier · 2013

This chapter contains sections titled: Definitions and metrics Connections between graphs, hypergraphs, and matrices Algorithms for hypergraph partitioning Purpose Conclusion Software references Bibliography

Cited by 0

Hypergraph Theory

Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho et al. · 2013

Cited by 1