Related papers: Specifying Graph Languages with Type Graphs
We introduce the idea of an n-simplex graph and games upon simplicial complexes. We then define moves on a labeled graph and pose the problem of whether given two labelings of a graph it is possible to change one into another via these…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…
A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms of presheaves on elementary graphs,…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
Large language models (LLMs) are increasingly used to complete complex tasks by selecting and coordinating external tools across multiple steps. This requires aligning tool choices with subtask intent while satisfying directional execution…
GP (for Graph Programs) is a rule-based, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from handling low-level data structures. The core of GP consists of four…
Graph models are helpful means of analyzing computer networks as well as complex system architectures for security. In this paper we evaluate the current state of research for representing and analysing cyber-attack using graph models, i.e.…
Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
We study twenty four written natural languages. We draw in the log scale, number of words starting with a letter vs rank of the letter, both normalised. We find that all the graphs are of the similar type. The graphs are tantalisingly…
Large language models have been extensively studied as neural knowledge bases for their knowledge access, editability, reasoning, and explainability. However, few works focus on the structural patterns of their knowledge. Motivated by this…
Graphs are an essential data structure utilized to represent relationships in real-world scenarios. Prior research has established that Graph Neural Networks (GNNs) deliver impressive outcomes in graph-centric tasks, such as link prediction…
The relationship between the concepts of network and knowledge graph is explored. A knowledge graph can be considered a special type of network. When using a knowledge graph, various networks can be obtained from it, and network analysis…
Large Language Models (LLMs) have garnered considerable interest within both academic and industrial. Yet, the application of LLMs to graph data remains under-explored. In this study, we evaluate the capabilities of four LLMs in addressing…
A recent paper by Drewes, Hoffmann, and Minas (GCM 2023 proceedings) has shown that certain graph languages can be defined and efficiently recognized by finite automata when strings over typed symbols are interpreted as graphs. This…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique…
We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…