26 papers · ranked by Valyu relevance
Steffen Klamt, Utz-Uwe Haus, Fabian Theis, Jörg Stelling
The understanding of biological networks is a fundamental issue in computational biology. When analyzing topological properties of networks, one often tends to substitute the term “network” for “graph”, or uses both terms interchangeably. From a mathematical perspective, this is often not fully correct, because many…
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.…
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…
Cliff Joslyn, Sinan G. Aksoy, Tiffany J Callahan, Lawrence Hunter + 4 more
'Brett Jefferson' 'Brenda Praggastis' 'Emilie Purvine' 'Ignacio J. Tripodi'] As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra…
Sinan G. Aksoy, Cliff Joslyn, Carlos Ortiz Marrero, Brenda Praggastis + 1 more
'Brenda Praggastis' 'Emilie Purvine'] We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include…
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…
Tin Lok James Ng, Thomas Brendan Murphy
A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the latent class analysis model that introduces two clustering structures for hyperedges and captures variation in the size of…
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…
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…
Florian Klimm, Charlotte M. Deane, Gesine Reinert
Protein-protein interactions are crucial in many biological pathways and facilitate cellular function. Investigating these interactions as a graph of pairwise interactions can help to gain a systemic understanding of cellular processes. It is known, however, that proteins interact with each other not exclusively in…
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…
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…
Ivo Baar, Lukas Hübner, Peter Oettig, Adrian Zapletal + 3 more
The so-called site repeats (SR) technique can be used to accelerate the widely-used phylogenetic likelihood function (PLF) by identifying identical patterns among multiple sequence alignment (MSA) sites, thereby omitting redundant calculations and saving memory. However, this complicates the optimal data distribution…
Tarun Kumar, Sankaran Vaidyanathan, Harini Ananthapadmanabhan, Srinivasan Parthasarathy + 1 more
'Srinivasan Parthasarathy' 'Balaraman Ravindran'] Clustering on hypergraphs has been garnering increased attention with potential applications in network analysis, VLSI design and computer vision, among others. In this work, we generalize the framework of modularity maximization for clustering on hypergraphs. To this…
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…
Marzieh Eidi, Jürgen Jost
Many empirical networks incorporate higher order relations between elements and therefore are naturally modelled as, possibly directed and/or weighted, hypergraphs, rather than merely as graphs. In order to develop a systematic tool for the statistical analysis of such hypergraph, we propose a general definition of…
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…
Giona Casiraghi, Vahan Nanumyan
A fundamental issue of network data science is the ability to discern observed features that can be expected at random from those beyond such expectations. Configuration models play a crucial role there, allowing us to compare observations against degree-corrected null-models. Nonetheless, existing formulations have…
Authors not listed
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…
Benedict Paten, Adam M Novak, Erik Garrison, Glenn Hickey
A superbubble is a type of directed acyclic subgraph with single distinct source and sink vertices. In genome assembly and genetics, the possible paths through a superbubble can be considered to represent the set of possible sequences at a location in a genome. Bidirected and biedged graphs are a generalization of…