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Probabilistic Graphical Bayesian models of causation have continued to impact on strategic analyses designed to help evaluate the efficacy of different interventions on systems. However, the standard causal algebras upon which these…
Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications. These justifications are expressed in terms of causal graphs…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
Network graphs have become a popular tool to represent complex systems composed of many interacting subunits; especially in neuroscience, network graphs are increasingly used to represent and analyze functional interactions between neural…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
It is not hard to find many complete bipartite graphs which are not determined by their spectra. We show that the graph obtained by deleting an edge from a complete bipartite graph is determined by its spectrum. We provide some graphs, each…
A self-contained graph is an infinite graph which is isomorphic to one of its proper induced subgraphs. In this paper, these graphs are studied by presenting some examples and defining some of their sub-structures such as removable…
A configuration of the triple $(\mathcal{P}, \mathcal{L}, \mathcal{I})$ on the incidence relation which holds the properties of "Any two points are incident with at most one line" and "Any two lines are incident with at most one point". In…
Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…
This work introduces a framework for quantifying the information content of logical propositions through the use of implication hypergraphs. We posit that a proposition's informativeness is primarily determined by its relationships with…
A graph $G$ with vertex set $V(G)$ and edge set $E(G)$ is said to be word-representable if there exists a word $w$ over the alphabet $V(G)$ such that, for any two distinct letters $x,y \in V(G)$, the letters $x$ and $y$ alternate in $w$ if…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
In this paper, we propose a model for building natural language explanations for Bayesian Network Reasoning in terms of factor arguments, which are argumentation graphs of flowing evidence, relating the observed evidence to a target…
This paper investigates the new notion of $2$-word-$\pi$-repre\-sentable graphs: the nodes of the graph correspond to the letters of the two words and there exists an edge between two nodes if the projections of any two letters of both…
We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension,…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…
"[M]athematicians care no more for logic than logicians for mathematics." Augustus de Morgan, 1868. Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional…