Related papers: Hermitian adjacency matrices of mixed multigraphs
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of a properly constructed matrix, and has found applications throughout science and technology. Many networks are multipartite, meaning…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
Hyperspectral unmixing aims at identifying a set of elementary spectra and the corresponding mixture coefficients for each pixel of an image. As the elementary spectra correspond to the reflectance spectra of real materials, they are often…
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…
Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the…
Here, we define a subdivision operation for a hypergraph and compute all the eigenvalues of the subdivision of regular and certain non-regular hypergraphs. In non-regular hypergraphs, we investigate the power of regular graphs, various…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
We present two hypermatrix formulations of the Cayley Hamilton theorem. One of the proposed formulation naturally extends to hypermatrices the combinatorial interpretations of the classical Cayley Hamilton theorem. We conclude by discussing…
Heterogeneous graph convolutional networks have gained great popularity in tackling various network analytical tasks on heterogeneous network data, ranging from link prediction to node classification. However, most existing works ignore the…
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods,…
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
There is a connection between *-representations of algebras associated with graphs and the problem about the spectrum of a sum of Hermitian operators (spectral problem). For algebras associated with extended Dynkin graphs we give an…
We study the balance of $G$-gain graphs, where $G$ is an arbitrary group, by investigating their adjacency matrices and their spectra. As a first step, we characterize switching equivalence and balance of gain graphs in terms of their…
A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge. In this article, first we establish bounds for…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
The eccentricity matrix $\epsilon(G)$, of a connected graph $G$ is obtained by retaining the maximum distance from each row and column of the distance matrix of $G$ and the other entries are assigned with 0. In this paper, we discuss the…
This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…
In recent years, unsupervised and self-supervised graph representation learning has gained popularity in the research community. However, most proposed methods are focused on homogeneous networks, whereas real-world graphs often contain…