Related papers: Link Algebra: A new aproach to graph theory
A network-theoretic approach for determining the complexity of a graph is proposed. This approach is based on the relationship between the linear algebra (theory of determinants) and the graph theory. In this paper we contribute a new…
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…
Multiplex networks allow us to study a variety of complex systems where nodes connect to each other in multiple ways, for example friend, family, and co-worker relations in social networks. Link prediction is the branch of network analysis…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
A graph is a structure composed of a set of vertices (i.e.nodes, dots) connected to one another by a set of edges (i.e.links, lines). The concept of a graph has been around since the late 19$^\text{th}$ century, however, only in recent…
We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
Today's data-heavy research environment requires the integration of different sources of information into structured data sets that can not be analyzed as simple matrices. We introduce an old technique, known in the European data analyses…
This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…
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…
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory…
In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality…
The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in…
Graph-structured data arise naturally in many different application domains. By representing data as graphs, we can capture entities (i.e., nodes) as well as their relationships (i.e., edges) with each other. Many useful insights can be…
Ontologies have been used for the purpose of bringing system and consistency to subject and knowledge areas. We present a criticism of the present mathematical structure of ontologies and indicate that they are not sufficient in their…
Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a…
We develop an algebraic theory of synchronous dataflow networks. First, a basic algebraic theory of networks, called BNA (Basic Network Algebra), is introduced. This theory captures the basic algebraic properties of networks. For…