2,017 Results Found

The category of directed graphs is isomorphic to a particular category whose objects are labeled undirected bipartite graphs and whose morphisms are undirected graph morphisms that respect the labeling. Based on this isomorphism, we begin by showing...

In this paper, we generalize the classical definition of Gromov hyperbolicity to the context of directed graphs and we extend one of the main results of the theory: the equivalence of the Gromov hyperbolicity and the geodesic stability. This theorem...

We use Category Theory to construct a ‘bridge’ relating directed graphs with undirected graphs, such that the notion of direction is preserved. Specifically, we provide an isomorphism between the category of simple directed graphs and a c...

Directed and weighted graphs can be used for many real-world applications to model and analyse the quality and structure of communication within the system, the distribution and flow of information, and various resources, dependencies, resilience, et...

With the widespread popularity of Wireless Mobile Networks (WMNs) in our daily life, the huge risk to disclose personal privacy of massive graph structure data in WMNs receives more and more attention. Particularly, as a special type of graph data in...

In this paper, we will classify the strongly minimal directed single graphs of 1-arity by axiomatizing the theory of characteristic sequence of such a graph. Then we will show this theory is complete by using Łos-Vaught test. Complete theory is...

In this paper, we introduce and study the Hardy–Littlewood maximal operator $M_{\overrightarrow{G}}$ on a finite directed graph $\overrightarrow{G}$. We obtain some optimal constants for the ${\ell }^p$ norm of $M_{\overrightarrow{G}}$ by introducing two classes of directed graphs.

In this paper, the authors establish the bounds for the Hardy-Littlewood maximal operator defined on a finite directed graph $\overrightarrow{G}$ in the space ${\mathrm{BV}}_p(\overrightarrow{G})$ of bounded p-variation functions. More precisely, the authors obtain the ${\mathrm{BV}}_p$ norms of $M_{\stackrel{\&ra}{G}}$...

Hamiltonian cycle problems play a central role in graph theory and have wide-ranging applications in network-on-chip architectures, interconnection networks, and large-scale parallel systems. When a network contains faulty nodes or faulty links, the...

We construct several new families of directed strongly regular Cayley graphs (DSRCGs) over the metacyclic group $M_{4n}=⟨a,b|a^n=b^4=1,b^{-1}ab=a^{-1}⟩$ , some of which generalize those ea...

Directed graphs can be prepared from big data containing peoples’ interaction information. In these graphs the vertices represent people, while the directed edges denote the interactions among them. The number of interactions at certain intervals can...

Uncertain graphs are commonly used to model the uncertain relationships between entities that arise from experimental or measurement errors. In recent years, the analysis of uncertain graphs has attracted significant research attention, with the comp...

Control Flow Graphs (CFGs) provide fundamental data for many program analyses, such as malware analysis, vulnerability detection, code similarity analysis, etc. Existing techniques for constructing control flow graphs include static, dynamic, and hyb...

General large language models (LLMs) often suffer from semantic misinterpretation, information redundancy, and hallucinated content when applied to educational question-answering tasks. These issues hinder their effectiveness in supporting students&r...

The rapid evolution of industrial components, the paradigm of Industry 4.0, and the new connectivity features introduced by 5G technology all increase the likelihood of cybersecurity incidents. Such incidents are caused by the vulnerabilities present...

Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and...

This article investigates the issue of observer-based adaptive time-varying formation-containment tracking (TVFCT) for multi-agent systems (MASs) with bounded unknown input in directed graphs. By applying estimated statuses of neighboring agents, two...

This paper introduces a novel fixed-point framework for orbital contractions within the setting of JS-metric spaces endowed with directed graphs. By relaxing conventional metric conditions and incorporating graph-theoretical structures, we define a n...

Detecting R-peak location is very important in electrocardiogram (ECG) analysis. Most existing algorithms focus on separating extreme data points to find R-peaks without ECG wave morphology consideration. As a result, we propose a new algorithm using...

Understanding and evaluating directed acyclic graphs (DAGs) is crucial for causal discovery, particularly in high-dimensional and small-sample datasets such as microbial abundance data. This study introduces DAGMetrics, an R package designed to compr...

A general lack of understanding pertaining to deep feedforward neural networks (DNNs) can be attributed partly to a lack of tools with which to analyze the composition of non-linear functions, and partly to a lack of mathematical models applicable to...

This paper deals with the consensus output tracking problem for multi-agent systems with unknown high-frequency gain signs, in which the subsystems are connected over directed graphs. The subsystems may have different dynamics, as long as the relativ...

The coordinated control of networked integrated energy systems (IESs) is complicated by the different response speeds of the electrical, gas, and thermal subsystems and by information exchange over directed communication graphs. Existing studies main...

Strategic evaluation is essential for decision-making under uncertainty. Yet existing qualitative and quantitative methods—including chat-oriented large language model (LLM) evaluations—are difficult to deploy in complex, dynamic environm...

It is well-known that the different products of graphs are some of the more symmetric classes of graphs. Since we are interested in hyperbolicity, it is interesting to study this property in products of graphs. Some previous works characterize the hy...

The worsening of housing problems in many countries has become a topic of global interest. Researchers point to a variety of factors that influence individual housing tenure decisions. Our study is based on longitudinal English Housing Survey (EHS) d...

Background: Tobacco use remains a leading preventable cause of morbidity and mortality in the United States, with persistent disparities in cessation outcomes across socioeconomic and racial groups. While numerous interventions exist, their effective...

In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. This property does not apply when we discretize spaces and continuous maps to directed graphs and their morphisms. In this paper, we give a con...

A new domination parameter in a fuzzy digraph is proposed to espouse a contribution in the domain of domination in a fuzzy graph and a directed graph. Let $G_D^{*}=\left(V,A\right)$ be a directed simple graph, where $V$ is a finite nonempty set and $A=\left\{\left(x,y\right):x,y\in V,x\ne y\right\}$. A fuz...

Knowledge graph embedding has been identified as an effective method for node-level classification tasks in directed graphs, the objective of which is to ensure that nodes of different categories are embedded as far apart as possible in the feature s...

In this manuscript, we introduce a few new types of dominations in intuitionistic fuzzy directed graphs (IFDGs) based on different types of strong arcs (SAs). Our work is not only a direct extension of domination in directed fuzzy graphs (DFGs) but a...

In various real-world scenarios, directed graphs can express the nature of relationships more clearly than undirected ones. Meanwhile, decentralized networks have attracted increasing attention in recent years. In decentralized directed networks (e.g...

Background/Objectives: Directed acyclic graphs (DAGs) inform the epidemiologic statistical modeling confounders to determine close to true causal relationships in a study context. They inform the inclusion of the predictive model variables that affec...

The topology of an interconnection network can be modeled by a graph $G=\left(V\right(G),E(G\left)\right)$. The connectivity of graph G is a parameter used to measure the reliability of a corresponding network. The direct product is an important graph product. This paper ma...

In the directed co-graph edge-deletion problem, we are given a directed graph and an integer k, and the question is whether we can delete, at most, k edges so that the resulting graph is a directed co-graph. In this paper, we make two minor contribut...

A chemical graph is an illustration of a chemical compound’s structural formula, where the edges indicate covalent bonding and the vertices depict atoms. In the study of (molecular) graphs, Zagreb indices and their variations are the most studi...

An $L(d,1)$-labeling of a graph $G=(V,E)$ is a function f from the vertex set $V\left(G\right)$ to the set of nonnegative integers such that the labels on adjacent vertices differ by at least d and the labels on vertices at distance two differ by at least one, where...

Mechanical, electrical, and plumbing (MEP) systems are crucial to a building, which directly affect the building safety, energy saving, and operational efficiency. Building information models (BIMs) help engineers to view the connection structure of...

This study examines the performance characteristics of four commonly used short-path algorithms, including Dijkstra, Bellman–Ford, Floyd–Warshall, and Dantzig, on randomly generated directed graphs. We analyze theoretical computational co...

In a previous paper we defined the black and white SAT problem which has exactly two solutions, where each variable is either true or false. We showed that black and white 2-SAT problems represent strongly connected directed graphs. We presented also...

Entity symmetry in teaching knowledge graphs is a characteristic of knowledge semantic expression and association, which plays a crucial role in the composition of knowledge structure. However, the evolution of the teaching knowledge graph may disrup...

Recently, there has been a dramatic rise in the demand for accurate temperature forecasts. However, challenges arise from modeling and fusing complex spatial and temporal features in temperature data. In this study, we propose a physics-informed dire...

The force-directed paradigm is one of the few generic approaches to drawing graphs. Since force-directed algorithms can be extended easily, they are used frequently. Most of these algorithms are, however, quite slow on large graphs, as they compute a...

Given a graph G without isolated vertices, a total Roman dominating function for G is a function $f:V\left(G\right)\to \{0,1,2\}$ such that every vertex u with $f\left(u\right)=0$ is adjacent to a vertex v with $f\left(v\right)=2$, and the set of vertices with positive labels induces a gr...

Given a directed graph, a k-hop reachability query, $u\stackrel{?k}{\to }v$, is used to check for the existence of a directed path from $u$ to $v$ that has a length of at most $k$. Addressing k-hop reachability queries is a fundamental task in graph theory and has been...

As an important branch of machine learning, recommendation algorithms have attracted the attention of many experts and scholars. The current recommendation algorithms all more or less have problems such as cold start and single recommended items. In...

In this work, we solve the problem of the coexistence of periodic orbits in homogeneous Boolean graph dynamical systems that are induced by a maxterm or a minterm (Boolean) function, with a direct underlying dependency graph. Specifically, we show th...

One of the main tasks in the field of directional statistics is to build goodness-of-fit tests for uniformity on circles, spheres or more abstract manifolds. We discuss a goodness-of-fit test for uniformity on a distance-regular graph. Our main tool...

There are many expressive visualization techniques for analyzing graphs. Yet, there is only little research on how existing visual representations can be employed to support data editing. An increasingly relevant task when working with graphs is the...

Precisely identifying cancer drivers helps us to understand the molecular mechanisms of cancer, offering critical targets for early diagnosis. Despite the increasing application of graph neural networks in predicting cancer driver genes, existing app...