Related papers: Abstract Orientable Incidence Structure and Algori…
Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independences, but different DAGs may encode the same set…
In this work we study the acyclic orientations of graphs. We obtain an encoding of the acyclic orientations of the complete $p$-partite graph with size of its parts $n_1,n_2,\ldots,n_p$ via a vector with $p$ symbols and length…
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…
The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical…
This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial…
Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The previous…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Given a graph and a representation of its fundamental group, there is a naturally associated twisted adjacency operator. The main result of this article is the fact that these operators behave in a controlled way under graph covering maps.…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
An ordinal-valued metric taking its values in the set of all countable ordinals can be assigned to a metrizable set of nodes in a transfinite graph. Then, a variety of results concerning nodal eccentricities, radii, diameters, centers,…
This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP…
We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized…
We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…
An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit…
By natural way the hierarchy structure is introduced on directed graphs with weighted adjacencies. Embedded system of algebras of subsets of the set of vertices of such digraph and it's consolidations, which vertices are the elementary sets…
We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
Acyclic networks are a class of complex networks in which links are directed and don't have closed loops. Here we present an algorithm for transforming an ordinary undirected complex network into an acyclic one. Further analysis of an…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
Current paper introduces a Hypergraph Graph model of data storage which can be represented as a hybrid data structure based on Hypergraph and Graph. The pro-posed data structure is claimed to realize complex combinatorial structures. The…