Results 51 to 60 of about 10,205 (230)

EasyHypergraph: an open-source software for fast and memory-saving analysis and learning of higher-order networks

Humanities & Social Sciences Communications
Higher-order relationships exist widely across different disciplines. In the realm of real-world systems, significant interactions involving multiple entities are common.
Bodian Ye, Min Gao, Xiu-Xiu Zhan, Xinlei He, Zi-Ke Zhang, Qingyuan Gong, Xin Wang, Yang Chen   +7 more
doaj   +1 more source

The signless Laplacian matrix of hypergraphs

Special Matrices, 2022
In this article, we define signless Laplacian matrix of a hypergraph and obtain structural properties from its eigenvalues. We generalize several known results for graphs, relating the spectrum of this matrix to structural parameters of the hypergraph ...
Cardoso Kauê, Trevisan Vilmar
doaj   +1 more source

Topology‐Aware Deep Learning on Higher‐Order Structures for Drug Response Prediction

Advanced Science, EarlyView.
We present TopDr, a topology‐aware deep learning framework that encodes both drugs and cell lines as multiscale simplicial complexes, capturing interactions at the 0‐, 1‐, and 2‐simplex levels. By jointly integrating local higher‐order neighborhoods and global topological structures, TopDr generates enriched representations for sensitivity prediction ...
Cong Shen, Guancen Lin, Chuan‐Shen Hu, Yong Wang   +3 more
wiley   +1 more source

Sheaf Hypergraph Networks [PDF]

, 2023
Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections.
Giulia Cassarà, Fabrizio Silvestri, Iulia Duta, Pietro Liò   +3 more
core  

Hypergraph burning

, 2023
Graph burning is a combinatorial game or process that models the spread of in uence throughout a network. We introduce a generalization of graph burning which applies to hypergraphs.
Jones, Caleb
core   +1 more source

Decompositions of complete 3-uniform hypergraphs into cycles of constant prime length [PDF]

Opuscula Mathematica, 2020
A complete \(3\)-uniform hypergraph of order \(n\) has vertex set \(V\) with \(|V|=n\) and the set of all \(3\)-subsets of \(V\) as its edge set. A \(t\)-cycle in this hypergraph is \(v_1, e_1, v_2, e_2,\dots, v_t, e_t, v_1\) where \(v_1, v_2,\dots, v_t\)
R. Lakshmi, T. Poovaragavan
doaj   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

On Tight Tree‐Complete Hypergraph Ramsey Numbers

Journal of Graph Theory, EarlyView.
ABSTRACT Chvátal showed that for any tree T $T$ with k $k$ edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1 $R(T,n)=k(n-1)+1$. For r = 3 $r=3$ or 4, we show that, if T $T$ is an r $r$‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ) $R(T,n)={\rm{\Theta }}({n}^{r-1})$.
Jiaxi Nie
wiley   +1 more source

Hypergraph-based connectivity measures for signaling pathway topologies

, 2019
Characterizing cellular responses to different extrinsic signals is an active area of research, and curated pathway databases describe these complex signaling reactions.
T. M. Murali (7548488), Anna Ritz (128202), Nicholas Franzese, Anna Ritz, Adam Groce, Nicholas Franzese (7548482), T M Murali, Adam Groce (7548485)   +7 more
core   +1 more source

Hyperbolic multi-channel hypergraph convolutional neural network based on multilayer hypergraph

Scientific Reports
In recent years, hypergraph neural networks have achieved remarkable success in tasks such as node classification, link prediction, and graph classification, thanks to their powerful computational capabilities.
Libing Bai, Feng Hu, Chunyang Tang, Zhangyu Mei, Chuang Liu   +4 more
doaj   +1 more source