Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit variety of downstream tasks as completion link prediction. However, existing embedding methods fell short provide systematic solution for the global c...

The thesis consists of two parts. In the first part we study two graph transformations,namely the Kelmans transformation and the generalized tree shift. In the second part of thisthesis we study an extremal graph theoretic problem and its relationship with algebraic graphtheory. The main results of this thesis are the following. • We show that the Kelmans transformation is a very ef...

Our goal is to use the properties of the adjacency/Laplacian matrix of graphs to first understand the structure of the graph and, based on these insights, to design efficient algorithms. The study of algebraic properties of graphs is called algebraic graph theory. One of the most useful algebraic properties of graphs are the eigenvalues (and eigenvectors) of the adjacency/Laplacian matrix.

The second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, plays a special role for the robustness of networks since it measures the extent to which it is difficult to cut the network into independent components. In this paper we study the behavior of the algebraic connectivity in a well-known complex network model, the Erdős-Rényi random graph. We estimat...

The second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, plays a special role for the robustness of complex networks since it measures the extent to which it is difficult to cut the network into independent components. In this paper we study the behavior of the algebraic connectivity in a well-known complex network model, the Erdős-Rényi random graph. We...

We report on implementing graph grammars for intelligence analysis in OCaml. Graph grammars are represented as elements of an algebraic data type in OCaml. In addition to algebraic data types, we use other concepts from functional programming languages to implement features of graph grammars. We use type checking to perform graph pattern matching. Graph transformations are defined as implicit c...

Let X > √ 2 be arbitrary. Is it possible to study right-reversible, integrable categories? We show that Q is larger than â. Unfortunately, we cannot assume that I (Γ) = |I|. Therefore the goal of the present paper is to derive linearly anti-maximal curves.

Feature graphs appearing in unification--based grammar formalisms and algebraic specifications of abstract data types (ADTs) are both used for defining a collection of objects together with functions between these object sets. Starting from this observation we define an algebraic semantics for feature graphs by assigning an algebraic specification to each feature graph. This opens the rich worl...

In this paper, we introduce a method of generating the dual graph of the minimal normal resolution of the algebraic curve singularities. Using factorization of polynomials over algebraic extension field, we can calculate the dual graph from the coefficients of the given polynomial exactly. The computing process includes no approximation. We constructed the system to generate the dual graph on R...

Exterior algebraic shifting and symmetric algebraic shifting of bipartite graphs and chordal graphs are studied in the present paper. keywords : Algebraic shifting, chordal graph.