18 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…
Yujie Zeng, Bo Liu, Fang Zhou, Linyuan Lü + 1 more
Null models are crucial tools for investigating network topological structures. However, research on null models for higher-order networks is still relatively scarce. In this study, we introduce an innovative method to construct null models for hypergraphs, namely the hyperedge swapping-based method. By preserving…
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.…
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…
Meilin Liu, Wenping Zheng, Shuxia Yuan, Jeng-Shyang Pan + 3 more
Hypergraph neural networks have shown strong potential for node classification due to their ability to capture high-order relationships and multi-granularity structural patterns. However, real-world hypergraphs are often sparse, which limits interaction modeling through node-hyperedge incidence and, in turn, weakens…
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…
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…
Henry-Louis de Kergorlay, Desmond J. Higham, Ginestra Bianconi, José F. F. Mendes
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie within a certain radius. From a modelling perspective, we explain how the model captures higher-order connections that arise…
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…
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…
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…
Leonie Neuhäuser, Michael Scholkemper, Francesco Tudisco, Michael T. Schaub
'Michael T. Schaub'] Dynamical systems on hypergraphs can display a rich set of behaviors not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much of this hypergraph structure is actually necessary to…
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…
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…
Zhe Yang, Liangkui Xu, Lei Zhao
Hypergraph learning is a new research hotspot in the machine learning field. The performance of the hypergraph learning model depends on the quality of the hypergraph structure built by different feature extraction methods as well as its incidence matrix. However, the existing models are all hypergraph structures built…
Hong-Yu Chen, Xiu-Juan Ma, Fu-Xiang Ma, Hai-Bing Xiao + 5 more
The internal structure of hyperedges has become central to understanding collective dynamics in hypernetworks. This study investigates the impact of hyperedge overlap on network synchronization when hyperedge structures are explicitly considered. We propose a modified hyper-adjacency matrix that captures the internal…
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…
Zhaoyang Wang, Xianghui Fu, Bo Deng, Yang Chen + 1 more
In algebraic topology, a k-dimensional simplex is defined as a convex polytope consisting of k + 1 vertices. If spatial dimensionality is not considered, it corresponds to the complete graph with k + 1 vertices in graph theory. The alternating sum of the number of simplices across dimensions yields a topological…