23 papers · ranked by Valyu relevance
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…
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…
Léo P M Diaz, Michael P H Stumpf, Pier Luigi Martelli
Graphs offer flexible ways to represent many biological systems. They are a well-established tool, and graph-based modeling formalisms such as chemical reaction networks and Petri nets have become widely used frameworks to describe and model such systems. Here, vertices are often taken to represent genes or gene…
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…
Jin-Li Guo, Qi Suo, Ai-Zhong Shen, Jeffrey Forrest
To depict the complex relationship among nodes and the evolving process of a complex system, a Bose-Einstein hypernetwork is proposed in this paper. Based on two basic evolutionary mechanisms, growth and preference jumping, the distribution of hyperedge cardinalities is studied. The Poisson process theory is used to…
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…
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…
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…
Amin Bahmanian, Mateja Šajna
In this paper we study fundamental connectivity properties of hypergraphs from a graph-theoretic perspective, with the emphasis on cut edges, cut vertices, and blocks. To prepare the ground, we define various types of subhypergraphs, as well as various types of walks in a hypergraph. We then prove a number of new…
Tamás-Zsolt Képes, Claudio Ardagna
Network analysis is an indispensable part of today’s academic field. Among the different types of networks, the more complex hypergraphs can provide an excellent challenge and new angles for analysis. This study proposes a variant of the critical node detection problem for hypergraphs using weighted node degree…
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…
Xavier Ouvrard
Hypergraphs were introduced in 1973 by Berge. This review aims at giving some hints on the main results that we can find in the literature, both on the mathematical side and on their practical usage. Particularly, different definitions of hypergraphs are compared, some unpublished work on the visualisation of large…
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…
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
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…
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…
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…
Rui Hou, Michael Small, Alistair R. R. Forrest
Cell-to-cell communication is mainly triggered by ligand-receptor activities. Through ligandreceptor pairs, cells coordinate complex processes such as development, homeostasis, and immune response. In this work, we model the ligand-receptor-mediated cell-to-cell communication network as a weighted directed hypergraph.…
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…
Authors not listed
Identifying synthesis routes from knowledge graphs poses challenges beyond retrosynthesis, including path–finding artifacts and data issues. We introduce “SynGPS”, a novel algorithm that overcomes these limitations by identifying viable routes even with common artifacts. SynGPS can resolve nonsensical cycles…
Authors not listed
A directed graph (or digraph) consists of a finite vertex set 𝑉 and a set of ordered edges 𝐸 ⊆ 𝑉 × 𝑉, each edge (𝑢, 𝑣) indicating a one-way connection from 𝑢 (source) to 𝑣 (target). A bidirected graph is a generalization of an undirected graph where each edge is assigned a direction at each of its endpoints…