Related papers: A matrix algebra for graphical statistical models
A connected graph can be associated with two distinct evolution algebras. In the first case, the structural matrix is the adjacency matrix of the graph itself. In the second case, the structural matrix is the transition probabilities matrix…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve…
An introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones.…
We consider the continuous-time quantum walk defined on the adjacency matrix of a graph. At each instant, the walk defines a mixing matrix which is doubly-stochastic. The average of the mixing matrices contains relevant information about…
Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. Associative arrays unify and simplify these different approaches into a common…
The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set of matrix-based graph operations that can…
The concept of directed strongly regular graphs was introduced by Duval in his paper, A Directed Graph Version of Strongly Regular Graphs. Duval also provided several construction methods for directed strongly regular graphs. The directed…
The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…
To apportion a complex matrix means to apply a similarity so that all entries of the resulting matrix have the same magnitude. We initiate the study of apportionment, both by unitary matrix similarity and general matrix similarity. There…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
We consider two graph invariants inspired by quantum walks- one in continuous time and one in discrete time. We will associate a matrix algebra called a cellular algebra with every graph. We show that, if the cellular algebras of two graphs…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
We introduce a new class of matroids, called graph curve matroids. A graph curve matroid is associated to a graph and defined on the vertices of the graph as a ground set. We prove that these matroids provide a combinatorial description of…
In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed,…
This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length $k$ in a graph with $N\geq k$ edges and no loops. Our proof relies on a construction of a number of terminating algorithms that…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
We introduce $C^*$-algebras associated with directed graphs, along with two generalizations of this concept, namely Exel-Pardo $C^*$-algebras associated with a self-similar action of a group on a directed graph, and the $C^*$-algebras…
Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…