Related papers: Hypergraph Analysis Based on a Compatible Tensor P…
We define graph products of families of pairs of groups and study the question when two such graph products are commensurable. As an application we prove linearity of certain graph products.
In this paper we present the super connectivity of Kronecker product of a general graph and a complete graph.
Personalization lies at the core of boosting the product search system performance. Prior studies mainly resorted to the semantic matching between textual queries and user/product related documents, leaving the user collaborative behaviors…
We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
We study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The $k$-token graph $F_k(G)$ of a graph $G$ is the graph whose vertices are the $k$-subsets of vertices from $G$,…
The Lagrangian density of an $r$-uniform hypergraph $H$ is $r!$ multiplying the supremum of the Lagrangians of all $H$-free $r$-uniform hypergraphs. For an $r$-uniform graph $H$ with $t$ vertices, it is clear that $\pi_{\lambda}(H)\ge…
We consider the algorithmic decision problem that takes as input an $n$-vertex $k$-uniform hypergraph $H$ with minimum codegree at least $m-c$ and decides whether it has a matching of size $m$. We show that this decision problem is fixed…
Multi-view learning has progressed rapidly in recent years. Although many previous studies assume that each instance appears in all views, it is common in real-world applications for instances to be missing from some views, resulting in…
A perfect structure is a triple $(M,P,S)$ of matrices $M, P$ and $S$ of consistent sizes such that $MP = PS$. Perfect structures comprise similar matrices, eigenvectors, perfect colorings (equitable partitions) and graph coverings. In this…
To achieve greater accuracy, hypergraph matching algorithms require exponential increases in computational resources. Recent kd-tree-based approximate nearest neighbor (ANN) methods, despite the sparsity of their compatibility tensor, still…
Observability of an array of identical LTI systems with incommensurable output matrices is studied, where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems. It is…
Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing. With focus on solution quality, we develop the first multilevel memetic algorithm to tackle the problem. Key components of our…
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
The increasing prevalence of relational data describing interactions among a target population has motivated a wide literature on statistical network analysis. In many applications, interactions may involve more than two members of the…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…
A common approach for analyzing hypergraphs is to consider the projected adjacency or Laplacian matrices for each order of interactions (e.g., dyadic, triadic, etc.). However, this method can lose information about the hypergraph structure…
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality…
The problem of finding the connected components of a graph is considered. The algorithms addressed to solve the problem are used to solve such problems on graphs as problems of finding points of articulation, bridges, maximin bridge, etc. A…