相关论文: Tensor join of hypergraphs and its spectra

Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we define function spaces and corresponding symmetric products…

In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…

We propose a theoretical framework of multi-way similarity to model real-valued data into hypergraphs for clustering via spectral embedding. For graph cut based spectral clustering, it is common to model real-valued data into graph by…

An oriented hypergraph is an oriented incidence structure that generalizes and unifies graph and hypergraph theoretic results by examining its locally signed graphic substructure. In this paper we obtain a combinatorial characterization of…

We propose a flexible framework for defining the 1-Laplacian of a hypergraph that incorporates edge-dependent vertex weights. These weights are able to reflect varying importance of vertices within a hyperedge, thus conferring the…

Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…

Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…

Copositivity of tensors plays an important role in vacuum stability of a general scalar potential, polynomial optimization, tensor complementarity problem and tensor generalized eigenvalue complementarity problem. In this paper, we propose…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian…

We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or…

In this paper, we compute normalized Laplacian spectra of central graph of a regular graph, central vertex join and central edge join of two regular graphs. Also, we determine their Kemeny's constant and degree Kirchhoff index.

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

The cut and join operations play important roles in tensor models in general. We introduce a generalization of the cut operation associated with the higher order variations and demonstrate how they generate operators in the Aristotelian…

For $\alpha \in [0,1]$, the $A_{\alpha}$-matrix of a graph $G$ is defined by $A_{\alpha}(G) = \alpha D(G) + (1- \alpha) A(G)$, where $A(G)$ and $D(G)$ denote the adjacency matrix and the diagonal degree matrix of $G$, respectively. In this…

Hypergraph Neural networks (HyperGNNs) and hypergraph signal denoising (HyperGSD) are two fundamental topics in higher-order network modeling. Understanding the connection between these two domains is particularly useful for designing novel…

Motivated by the PageRank model for graph partitioning, we develop an extension of PageRank for partitioning uniform hypergraphs. Starting from adjacency tensors of uniform hypergraphs, we establish the multi-linear pseudo-PageRank (MLPPR)…

We introduce and study tropical eigenpairs of tensors, a generalization of the tropical spectral theory of matrices. We show the existence and uniqueness of an eigenvalue. We associate to a tensor a directed hypergraph and define a new type…

We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph. We study their H$^+$-eigenvalues, i.e., H-eigenvalues with nonnegative H-eigenvectors, and H$^{++}$-eigenvalues, i.e.,…

The absence of intrinsic adjacency relations and orientation systems in hypergraphs creates fundamental challenges for constructing sheaf Laplacians of arbitrary degrees. We resolve these limitations through symmetric simplicial sets…