Related papers: Link Algebra: A new aproach to graph theory

We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…

We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The…

Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be "trained" on large knowledge graphs, and then used…

This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…

Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…

There are countless sources of data available to governments, companies, and citizens, which can be combined for good or evil. We analyse the concepts of combining data from common sources and linking data from different sources. We model…

In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…

We introduce a broad class of equations that are described by a graph, which includes many well-studied systems. For these, we show that the number of solutions (or the dimension of the solution set) can be bounded by studying certain…

Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and…

Many interesting examples of operator algebras, both self-adjoint and non-self-adjoint, can be constructed from directed graphs. In this survey, we overview the construction of $C^*$-algebras from directed graphs and from two…

Effectively showing the relationships between objects in a dataset is one of the main tasks in information visualization. Typically there is a well-defined notion of distance between pairs of objects, and traditional approaches such as…

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…

In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the…

The concept of multilayer networks has become recently integrated into complex systems modeling since it encapsulates a very general concept of complex relationships. Biological pathways are an example of complex real-world networks, where…

A link stream is a set of possibly weighted triplets (t, u, v) modeling that u and v interacted at time t. Link streams offer an effective model for datasets containing both temporal and relational information, making their proper analysis…

Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…

Previous work has axiomatised the cardinality operation in relation algebras, which counts the number of edges of an unweighted graph. We generalise the cardinality axioms to Stone relation algebras, which model weighted graphs, and study…

deepstruct connects deep learning models and graph theory such that different graph structures can be imposed on neural networks or graph structures can be extracted from trained neural network models. For this, deepstruct provides deep…