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A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
We study some subsets of rational points in an algebraic groups defined by open conditions on their projection in the finite adeles points. Using adelic mixing we are able to prove an equidistribution's result for the projection of these…
How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
A symmetric $m\times m$ matrix $M$ with entries taken from $\{0,1,\ast\}$ gives rise to a graph partition problem, asking whether a graph can be partitioned into $m$ vertex sets matched to the rows (and corresponding columns) of $M$ such…
We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all…
In this article, we establish a mathematical framework that utilizes concepts from graph theory to formalize the parity transformation, an encoding strategy for compiling optimization problems on quantum devices. We introduce the…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
We introduce the concept of Almost-Companion Matrix (ACM) by relaxing the non-derogatory property of the standard Companion Matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and…
Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional…
We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…
The concept of Loewner (partial) order for general complex matrices is introduced. After giving the definition of arithmetic, geometric, and harmonic mean for accretive-dissipative matrices, we study their basic properties. An AM-GM-HM…
For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…
Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel…
Graph machine learning architectures are typically tailored to specific tasks on specific datasets, which hinders their broader applicability. This has led to a new quest in graph machine learning: how to build graph foundation models…
We provide a graphical calculus for computing averages of tensor network diagrams with respect to the distribution of random vectors containing independent uniform complex phases. Our method exploits the order structure of the partially…
A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…