26 papers · ranked by Valyu relevance
Youjia Zhou, Archit Rathore, Emilie Purvine, Bei Wang
—We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to its graph representations known as the line graph and clique expansion. A…
S. M. Shovan, Arindam Khanda, Sanjukta Bhowmick, Sajal K. Das
—Higher-order interactions beyond pairwise relationships in large complex networks are often modeled as hypergraphs. Analyzing hypergraph properties such as triad counts is essential, as hypergraphs can reveal intricate group interaction patterns that conventional graphs fail to capture. In realworld scenarios, these…
Samuel Barton, Zoe Broad, Daniel Ortiz-Barrientos, Diane Donovan + 1 more
Multidisciplinary approaches can significantly advance our understanding of complex systems. For instance, gene co-expression networks align prior knowledge of biological systems with studies in graph theory, emphasising pairwise gene to gene interactions. In this paper, we extend these ideas, promoting hypergraphs as…
Sarah Lawson, Diane Donovan, James Lefevre, Irene Sendiña-Nadal
The use of graph centrality measures applied to biological networks, such as protein interaction networks, underpins much research into identifying key players within biological processes. This approach however is restricted to dyadic interactions and it is well-known that in many instances interactions are polyadic.…
Etab Mohammed Alotaibi, Omer S. Alkhnbashi, Van Dinh Tran
Cancer development is driven by a small subset of somatic mutations, known as driver mutations, that disrupt key regulatory processes in cells. These mutations occur in specific genes, called cancer driver genes, whose altered functions promote tumor initiation and progression. Accurately identifying driver genes…
Mario Pascual-Gonzalez, Ezequiel Lopez-Rubio
We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $Σ_{\mathrm{HG}}$. The encoding is executed by a small virtual machine comprising a sparse hypergraph, a circular doubly-linked list (CDLL) of node…
Hanyu Xie, Changjian Song, Hao Shao, Lunwen Wang + 1 more
Hyperedge prediction is crucial for uncovering higher-order relationships in complex systems but faces core challenges, including unmodeled node influence heterogeneity, overlooked hyperedge order effects, and data sparsity. This paper proposes Order propagation Fusion Self-supervised learning for Hyperedge prediction…
C. Gaucherel, M. Cosme, C. Noûs, F. Pommereau
To understand and manage (social-)ecological systems, we need an intuitive and rigorous way to represent them. Recent ecological studies propose to represent interaction networks into modular graphs, multiplexes and higher-order interactions. Along these lines, we argue here that non-dyadic (non-pairwise) interactions…
Yazeed Alkhrijah, Abbas N. Talib, Narinderjit Singh Sawaran Singh, Ashraf Abed Hussein
Food recommendation systems face fundamental challenges in modeling the complex, compositional relationships among users, foods, and ingredients. Traditional collaborative filtering and Graph Neural Networks rely on pairwise connections that oversimplify culinary interactions, while existing hypergraph approaches use…
Marc Barthélemy
Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we introduce a class of models for random hypergraphs which displays a similar level of…
Marco Mancastroppa, Iacopo Iacopini, Giovanni Petri, Alain Barrat
Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We consider the decomposition of a hypergraph in hyper-cores, subsets of nodes…
Daniel T. Chang
Chemical Hypergraph Authors: ['Daniel T. Chang'] Abstract: The conventional definition of hypergraph has two major issues: (1) there is not a standard definition of directed hypergraph and (2) there is not a formal definition of nested hypergraph. To resolve these issues, we propose a new definition of hypergraph that…
Dalma Bilbao, Hugo Aimar, Pablo Torterolo, Diego M. Mateos
Higher-Order Interaction (HOI) theory offers a powerful framework for capturing complex, non-linear relationships within multidimensional systems, moving beyond traditional pairwise graph methods to encompass multi-way interactions. This study applies HOI analysis, specifically using hypergraph theory, to explore…
Takaaki Fujita
Theoretical Foundations Authors: ['Takaaki Fujita'] In the context of handling uncertainty, concepts such as Fuzzy Graphs and Neutrosophic Graphs have gained prominence. It is well established that Plithogenic Graphs serve as a generalization of both Fuzzy Graphs and Neutrosophic Graphs. Furthermore, the Fuzzy Graph…
Authors not listed
We present a unified, set–theoretic framework that extends molecular graphs to hypergraphs and superhypergraphs via iterated power sets. We define Molecular Graphs, Molecular HyperGraphs, and Molecular SuperHyperGraphs, and develop four complements over them: Weighted, Rough, Neural, and Multipolar frameworks. We prove…
Yihe Deng, Ruochi Zhang, Pan Xu, Jian Ma + 1 more
Hypergraphs are powerful tools for modeling complex interactions across various domains, including biomedicine. However, learning meaningful node representations from hypergraphs remains a challenge. Existing supervised methods often lack generalizability, thereby limiting their real-world applications. We propose a…
Authors not listed
Graph theory provides a framework for clearly representing relationships between objects [1,2]. In the fields of chemistry and biology, graph-based concepts are widely applied. Hypergraphs generalize classical graphs by allowing hyperedges to connect any nonempty subset of vertices [3]. Superhypergraphs extend this…
Deepak Maurya, Balaraman Ravindran, Ilya Safro
Hypergraphs have gained increasing attention in the machine learning community lately due to their superiority over graphs in capturing super-dyadic interactions among entities. In this work, we propose a novel approach for the partitioning of k-uniform hypergraphs. Most of the existing methods work by reducing the…
Amal S. Alali, Esra Öztürk Sözen, Cihat Abdioğlu, Shakir Ali + 1 more
'Elif Eryaşar'] Topological indices are numerical parameters that indicate the topology of graphs or hypergraphs. A hypergraph $H=(V(H),E(H))$ consists of a vertex set $V(H)$ and an edge set $E(H)$, where each edge $e\inE(H)$ is a subset of $V(H)$ with at least two elements. In this paper, our main aim is to introduce…
Zehui Li, Xiangyu Zhao, Mingzhu Shen, Guy‐Bart Stan + 2 more
'Yiren Zhao'] Graphs are widely used to encapsulate a variety of data formats, but real-world networks often involve complex node relations beyond only being pairwise. While hypergraphs and hierarchical graphs have been developed and employed to account for the complex node relations, they cannot fully represent these…
Martina Contisciani, Federico Battiston, Caterina De Bacco
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to characterize the structural organization of hypergraphs. The method allows to…
Md Ishtyaq Mahmud, Tania Banerjee
We propose HyperNiche, a hypergraph-based framework for modeling higher-order, heterogeneous cellular niches from spatial transcriptomics data. Unlike conventional graph-based methods that rely on pairwise similarity and tend to produce homogeneous clusters, HyperNiche learns anchor-centered hyperedges through a…
Chao Deng, Hong-Dong Li, Li-Shen Zhang, Yi-Wei Liu + 2 more
Identifying cancer genes remains a significant challenge in cancer genomics research. Annotated gene sets encode functional associations among multiple genes, and cancer genes have been shown to cluster in hallmark signaling pathways and biological processes. The knowledge of annotated gene sets is critical for…
Authors not listed
Curried functions provide a systematic way of transforming multi-argument functions into nested singleargument functions. This transformation allows partial application and supports many central principles of functional programming. Their extension, called curried 𝑘-ary functions, naturally generalizes the familiar…
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The concept of aClassical Structure provides a broad mathematical framework, whereas a Hyperstructure arises via the powerset construction, and an 𝑛-Superhyperstructure is obtained by iterating this construction n times [1]. Intuitively, the n-th powerset corresponds to 𝑛 successive applications of the powerset…
Authors not listed
Genetic Algorithms are a powerful method to solve optimization problems with complex cost functions over vast search spaces that rely in particular on recombining parts of previous solutions. Crossover operators play a crucial role in this context. Here, we describe a large class of these operators designed for…