Related papers: Identifying Self-Amplifying Hypergraph Structures …
In this paper we solve the problem of finding in a given weighted hypergraph a subhypergraph with a maximum possible density. We introduce the notion of a support matrix and prove that the density of an optimal subhypergraph is equal to…
Aiming at the problem that existing methods could not fully capture the intrinsic structure of data without considering the higher-order neighborhood information of the data, we proposed an unsupervised feature selection algorithm based on…
Algebraic connectivity is one way to quantify graph connectivity, which in turn gauges robustness as a network. In this paper, we consider the problem of maximising algebraic connectivity both local and globally over all simple, undirected,…
In multi-agent systems, strong connectivity of the communication network is often crucial for establishing consensus protocols, which underpin numerous applications in decision-making and distributed optimization. However, this connectivity…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
Most existing approaches for community detection require complete information of the graph in a specific scale, which is impractical for many social networks. We propose a novel algorithm that does not embrace the universal approach but…
This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex…
Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering…
This paper presents a machine learning-based framework for topology optimization of self-supporting structures, specifically tailored for additive manufacturing (AM). By employing a graph neural network (GNN) that acts as a neural field…
Self-supervised auto-encoders have emerged as a successful framework for representation learning in computer vision and natural language processing in recent years, However, their application to graph data has been met with limited…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
Graph representation learning has attracted increasing research attention. However, most existing studies fuse all structural features and node attributes to provide an overarching view of graphs, neglecting finer substructures' semantics,…
Symmetries found through automorphisms or graph fibrations provide important insights in network analysis. Symmetries identify clusters of robust synchronization in the network which improves the understanding of the functionality of…
We propose a tensor product structure that is compatible with the hypergraph structure. We define the algebraic connectivity of the $(m+1)$-uniform hypergraph in this product, and prove the relationship with the vertex connectivity. We…
Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…
Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…
A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
Machine learning algorithms have made remarkable achievements in the field of artificial intelligence. However, most machine learning algorithms are sensitive to the hyper-parameters. Manually optimizing the hyper-parameters is a common…
We study finite-sum nonlinear programs with localized variable coupling encoded by a (hyper)graph. We introduce a graph-compliant decomposition framework that brings message passing into continuous optimization in a rigorous, implementable,…