Basic Graph Research Articles

Measuring economic graph competence

The ability to work with graphs is at the core of the economic domain and is also one of the central challenges for novices in the field. To accurately assess the graph competence of higher education students, we developed and tested an 18-item graph competence instrument with different economics graphs. The sample consisted of 579 students from multiple higher education institutions in southwestern Germany. Our findings reveal that while students generally perform well on basic graph operations, they struggle with complex tasks such as comparing quantities and understanding economic implications, particularly with supply and demand models and indifference curves. The results highlight the need for instructional focus on integrating graph reading with economic concepts and provide a diagnostic tool for further research. The study underscores the challenges faced by learners, especially those with limited economic background and female students, and offers insights for improving economic graph education.

Fractional Vertex Cover Reliability of Graphs

Let G be a graph and let 0 ≤ p , q and p + q ≤ 1 . Suppose that each vertex of G gets a weight of 1 with probability p , 1 2 with probability q , and 0 with probability 1 − p − q , and vertex weight probabilities are independent. The \textit{fractional vertex cover reliability} of G , denoted by FRel ( G ; p , q ) , is the probability that the sum of weights at the end-vertices of every edge in G is at least 1 . In this article, we first provide various computational formulas for FRel ( G ; p , q ) considering general graphs, basic graphs, and graph operations. Secondly, we determine the graphs which maximize FRel ( G ; p , q ) for all values of p and q in the classes of trees, connected unicyclic and bicyclic graphs with fixed order, and determine the graphs which minimize it in the classes of trees and connected unicyclic graphs with fixed order. Our results on optimal graphs extend some known results in the literature about independent sets, and the tools we developed in this paper have the potential to solve the optimality problem in other classes of graphs as well.

On the Independent Uphill Domination Polynomial of a Graph

Objectives: The concept of independent uphill domination polynomial is newly defined to deal with the present graph theory in this paper. It is characterized and analyzed within various contexts and types of graphs, its roots are discovered, its relation to different graph transforms is discussed and the study of this graph can help reveal new structures of graphs. Methods: The independent uphill domination polynomial is defined as is an independent uphill dominating set of size in . The uphill paths are used in identifying the criterion of independent uphill dominating sets. The computation of specific values of the polynomial is performed for basic graphs, and the polynomial’s response to various flip operations is observed. Findings: Checking the standard graphs for some properties of the independent uphill dominance polynomial shows the features of the independent uphill dominance polynomial as an uphill dominance polynomial of a certain type of digraph. Families of polynomials can be best understood when it comes to stability and characteristics by analyzing their roots on different graphical planes. They demonstrate how the structure of the graph and the polynomial change as a result of the different graph operations. Novelty: Incorporating uphill paths into independent dominating sets extends common domination polynomials and provides a distinct perspective distinct from previous investigations on graph dominance. Hence, this work enriches the subject and suggests new avenues for studying related polynomials and their uses by encompassing more structural properties of graphs. Keywords: Domination, Polynomial, Uphill domination, Independent domination, Root, Book graph, Independent uphill domination polynomial

Exploring ncRNA-Drug Sensitivity Associations via Graph Contrastive Learning.

Increasing evidence has shown that noncoding RNAs (ncRNAs) can affect drug efficiency by modulating drug sensitivity genes. Exploring the association between ncRNAs and drug sensitivity is essential for drug discovery and disease prevention. However, traditional biological experiments for identifying ncRNA-drug sensitivity associations are time-consuming and laborious. In this study, we develop a novel graph contrastive learning approach named NDSGCL to predict ncRNA-drug sensitivity. NDSGCL uses graph convolutional networks to learn feature representations of ncRNAs and drugs in ncRNA-drug bipartite graphs. It integrates local structural neighbours and global semantic neighbours to learn a more comprehensive representation by contrastive learning. Specifically, the local structural neighbours aim to capture the higher-order relationship in the ncRNA-drug graph, while the global semantic neighbours are defined based on semantic clusters of the graph that can alleviate the impact of data sparsity. The experimental results show that NDSGCL outperforms basic graph convolutional network methods, existing contrastive learning methods, and state-of-the-art prediction methods. Visualization experiments show that the contrastive objectives of local structural neighbours and global semantic neighbours play a significant role in contrastive learning. Case studies on two drugs show that NDSGCL is an effective tool for predicting ncRNA-drug sensitivity associations.

The diameter of sum basic equilibria games

We study the sum basic network creation game introduced in 2010 by Alon, Demaine, Hajiaghai and Leighton. In this game, an undirected and unweighted graph G is said to be a sum basic equilibrium if and only if, for every edge uv and any vertex v′ in G, swapping edge uv with edge uv′ does not decrease the total sum of the distances from u to all the other vertices. This concept lies at the heart of the network creation games, where the central problem is to understand the structure of the resulting equilibrium graphs, and in particular, how well they globally minimize the diameter. In this sense, in 2013 Alon et al. showed an upper bound of 2O(log⁡n) on the diameter of sum basic equilibria, and they also proved that if a sum basic equilibrium graph is a tree, then it has diameter at most 2. In this paper, we prove that the upper bound of 2 also holds for bipartite graphs and even for some non-bipartite classes like block graphs and cactus graphs.

A linear algorithm for radio k-coloring of powers of paths having small diameters

The radio k-chromatic number rck(G) of a graph G is the minimum integer λ such that there exists a function ϕ:V(G)→{0,1,⋯,λ} satisfying |ϕ(u)−ϕ(v)|≥k+1−d(u,v), where d(u,v) denotes the distance between u and v. A considerable amount of attention has been given to find the exact values or providing polynomial time algorithms to determine rck(G) for several basic graph families such as paths, cycles, trees, and powers of paths, usually for some specific values of k. In this article, we find the exact values of rck(G) where G is a power of a path with diameter strictly less than k. Our proof readily provides a linear time algorithm for assigning a radio k-coloring of G. Furthermore, our proof technique is a potential tool for solving the same problem for other classes of graphs having “small” diameters.

Fake review detection with label-consistent and hierarchical-relation-aware graph contrastive learning

The rapid increase in fake reviews in e-commerce presents a considerable challenge, as it misleads consumers and compromises market integrity. Recently, graph-based models for detecting fake reviews have emerged as promising solutions. However, conventional methods and basic graph neural network techniques often fail to recognize the deceptive tactics of fraudsters, negatively affecting their efficacy. In response, we propose the label-consistent and hierarchical-relation-aware graph contrastive learning (LRGCL) framework, which is specifically designed to identify fake reviews, even when fraudsters employ various disguises. This framework implements a label-consistent graph contrastive learning approach to distinctly identify positive and negative samples, ensuring clear separation between authentic and fraudulent nodes despite feature camouflage. Additionally, LRGCL classifies negative samples into several categories using a hierarchical approach that leverages relationships within a multi-relation graph, thereby counteracting relation camouflage. The integration of these two strategies significantly reduces the effectiveness of these camouflages, leading to more precise detection of fake reviews. Empirical tests using real-world datasets validate the superior efficacy of LRGCL, as it surpasses current leading methods across key performance metrics.

Research on inter-well connectivity of water-flooding reservoir: Temporal neural network based on graph structure

Inter-well connectivity plays a crucial role in the development and production of water-flooding reservoirs, involving fluid transfer and mutual influence between different wells, and playing an important role in optimizing oilfield development and production. The traditional study of inter-well connectivity is mainly based on static information, while ignoring the dynamic changes over time and the graph structure of the well network. To address this issue, this paper proposes a temporal neural network based on graph structure (GSTNN). It combines the advantages of traditional neural networks and graph structures, fully considering the temporal information of the well network. A series of well network temporal feature information is used to predict inter-well connectivity within the framework of traditional neural networks, and optimize the model based on the graph structure of the well network. Experiments with GSTNN in different basic models and different graph sizes show that the method proposed in this paper is consistent with the actual geological characteristics of oil reservoirs. Compared with traditional neural network methods, GSTNN achieves more accurate results and shows good performance in less time in production prediction and inter-well connectivity reflection.

Computational analysis of GCaMP fluorescence data in neuronal activity

The background and motivation of our research is to explore how to use computational methods to analyze GCaMP fluorescence data. GCaMP is a genetically encoded calcium indicator that can be used to observe the activity of thousands of neurons simultaneously using modern fluorescence imaging techniques. Our research includes the application of principles such as basic signal processing, statistical inference, hypothesis testing, and graph theory to help understand raw GCaMP fluorescence data recorded from awake, behavioral mice. The data set includes GCaMP fluorescence trace and correlation coefficient matrix among neurons. Our methods include high-pass filtering, Gaussian mixture model fitting and online active set method peak inference (oasis). By analyzing the correlation between neurons, we can understand the connection and centrality between neurons.

Analysis of Mixed Traffic Flow Characteristics Based on Fleet Composition

In urban road networks, the integration of connected and autonomous vehicles (CAV) significantly influences traffic flow patterns, with the Fleet Composition—representing the positioning of these vehicles within convoys—being crucial in dictating the symmetry of information exchange amongst them. First, the vehicle composition of the mixed traffic flow is analyzed, and the mathematical analytical expressions of the random distribution characteristics of different types of vehicles are constructed. Second, we analyze the vehicle according to human characteristics in different situations. Then, consider the following characteristics and reaction times of manual drivers, establish a mixed traffic flow following model, and validate the established following. Finally, the basic graph model considering Fleet Composition is derived, and the effects of reaction time, Fleet Composition, driver following characteristics, and other parameters on road capacity under different penetration rates of CAV are analyzed by a Python and SUMO joint simulation. Finally, the characteristics of mixed traffic flow at intersections were analyzed.

Properties of the Laplacian spectra of certain basic and hierarchical graphs

Properties of the Laplacian spectra of certain basic and hierarchical graphs

Self-supervised BGP-graph reasoning enhanced complex KBQA via SPARQL generation

Knowledge base question answering aims to answer complex questions from large-scale knowledge bases. Although existing generative language models that translate questions into SPARQL queries have achieved promising results, there are still generation errors due to redundancies or errors in the knowledge fed to the generative models and difficulties in representing the implicit logic of knowledge as the specific syntax of SPARQL. To address above issues, we propose TrackerQA, a novel self-supervised reasoning framework based on basic graph patterns (BGP) to determine precise paths and enhance SPARQL generation. First, we develop a contrastive learning semantic matching model to reduce the large knowledge searching space. Then, we built a BGP parser that parses the recalled knowledge and constraints into BGP graphs, which can deconstruct complex knowledge into BGP triples and naturally obtain supervision from gold SPARQL. Next, we design a self-supervised BGP graph neural network that encodes knowledge through graph transformation layers with directed message-passing control and employs a question-aware attention mechanism to predict the exact BGP paths. Finally, a SPARQL generator integrates the paths into a pre-trained language model to improve the performance of SPARQL generation. Experiments on the KQA Pro dataset show that our model achieves state-of-the-art answering accuracy scores of 95.32%, being the closest to the human level at 97.5%, and reasons out KB paths with F1 scores of 0.98 for nodes and 0.99 for edges.

Proactive enforcement of provisions and obligations

We present an approach to the proactive enforcement of provisions and obligations, suitable for building policy enforcement mechanisms that both prevent and cause system actions. Our approach encompasses abstract requirements for proactive policy enforcement, a system model describing how enforcement mechanisms interact with and control target systems, and concrete policy languages and associated enforcement mechanisms. As examples of policy languages, we consider finite automata and timed dynamic condition response (DCR) graphs. We use finite automata to illustrate the basic principles and DCR graphs to show how these principles can be adapted to a practical, real-time policy language. In both cases, we show how to algorithmically determine whether a given policy is enforceable and, when this is the case, construct an associated enforcement mechanism. Our approach improves upon existing formalisms in two ways: (1) we exploit the target system’s existing functionality to avert policy violations proactively, rather than compensate for them reactively; and (2) rather than requiring the manual specification of remedial actions in the policy, we deduce required actions directly from the policy.

The Role of Data Visualization in Decision Making – Case of D-mart

Data visualization is crucial for informed decision-making in today's data-driven world. It transforms complex data sets into visually engaging representations, enhancing cognitive processes and fostering insights. The report explores the principles, tools, and impact of data visualization, highlighting its ability to streamline operations, identify market trends, optimize resource allocation, and mitigate risks. It provides an overview of various data visualization tools and types, ranging from basic charts and graphs to advanced interactive dashboards and geospatial visualizations. Organizations can leverage these tools to gain a competitive edge and make informed decisions that drive sustainable success. By harnessing the power of visual analytics, decision-makers can make informed choices that drive business growth and innovation.

Signed graphs with exactly two distinct main eigenvalues

An eigenvalue λ of a signed graph S of order n is a main eigenvalue if its eigenspace is not orthogonal to the all-ones vector j. Characterizing signed graphs with exactly k(1≤k≤n) main eigenvalues is a problem in algebraic and graph theory that has been studied since 2020. Z. Stanić has noticed that a signed graph has exactly one main eigenvalue if and only if it is net-regular, and in this paper, we study signed graphs with exactly two distinct main eigenvalues by studying (0,1,2)-multi-graphs with exactly two distinct main eigenvalues. We partially characterize the case when the basic graphs of the (0,1,2)-multi-graphs are trees, and propose some problems for further research.

Human learning of hierarchical graphs.

Humans are exposed to sequences of events in the environment, and the interevent transition probabilities in these sequences can be modeled as a graph or network. Many real-world networks are organized hierarchically and while much is known about how humans learn basic transition graph topology, whether and to what degree humans can learn hierarchical structures in such graphs remains unknown. We probe the mental estimates of transition probabilities via the surprisal effect phenomenon: humans react more slowly to less expected transitions. Using mean-field predictions and numerical simulations, we show that surprisal effects are stronger for finer-level than coarser-level hierarchical transitions, and that surprisal effects at coarser levels are difficult to detect for limited learning times or in small samples. Using a serial response experiment with human participants (n=100), we replicate our predictions by detecting a surprisal effect at the finer level of the hierarchy but not at the coarser level of the hierarchy. We then evaluate the presence of a trade-off in learning, whereby humans who learned the finer level of the hierarchy better also tended to learn the coarser level worse, and vice versa. This study elucidates the processes by which humans learn sequential events in hierarchical contexts. More broadly, our work charts a road map for future investigation of the neural underpinnings and behavioral manifestations of graph learning.

Neighborhood contrastive learning-based graph neural network for bug triaging

Researchers have been developing automatic bug triaging techniques by leveraging bug information sourced from bug tracking systems. Recent studies have modeled the bug-developer relationship as a graph, introducing graph neural networks for bug triaging. Despite achieving positive outcomes, these methods overlook issues related to data sparsity and fail to fully exploit implicit relationships within the graph. In addressing these challenges, we present the Neighborhood Contrastive Learning-based Graph Neural Network Bug Triaging framework, abbreviated as NCGBT. Our approach models the relationship between bugs and developers as a bipartite graph. We utilize a pre-trained language model to acquire the initial representation of bug nodes. Employing a basic graph neural network framework, we learn the representation of all nodes and leverage these representations to predict developers for a given bug. Our proposed strategy involves neighborhood contrastive learning applied to the basic graph neural network approach. We take into account the neighbors of nodes from both structural and semantic perspectives, utilizing them as contrastive objects. Extensive experiments conducted on three public datasets demonstrate the effectiveness of the NCGBT framework.

GNNCL: A Graph Neural Network Recommendation Model Based on Contrastive Learning

In the field of recommendation algorithms, the representation learning for users and items has evolved from using single IDs or historical interactions to utilizing higher-order neighbors. This can be achieved by modeling the user–item interaction graph to capture user preferences for items. Despite the promising results achieved by these algorithms, they still suffer from the issue of data sparsity. In order to mitigate the impact of data sparsity, contrastive learning has been adopted in graph collaborative filtering to enhance performance. However, current recommendation algorithms using contrastive learning yield uneven representations after data augmentation and do not consider the potential relationships among users (or items). To address these challenges, we propose a graph neural network-based recommendation model that integrates contrastive learning (GNNCL). This model combines data augmentation with added noise and the exploration of semantic neighbors for nodes. For the structural neighbors on the interaction graph, we introduce a novel and straightforward contrastive learning approach, abandoning previous graph augmentation methods, and introducing uniform noise into the embedding space to create contrastive views. To unearth potential semantic neighbor relationships in the semantic space, we assume that users with similar representations possess semantic neighbor relationships and merge these semantic neighbors into the prototype contrastive learning. We utilize a clustering algorithm to obtain prototypes for users and items and employ the EM algorithm for prototype contrastive learning. Experimental results validate the effectiveness of our approach. Particularly, on the Yelp2018 and Amazon-book datasets, our method exhibits significant performance improvements compared to basic graph collaborative filtering models.

Prediction of Mechanical Properties of Cold-Rolled Steel Based on Improved Graph Attention Network

The prediction of mechanical properties of cold-rolled steel is very important for the quality control, process optimization, and cost control of cold-rolled steel, but it is still a challenging task to predict accurately. For the existing graph structure of graph attention networks, it is difficult to effectively establish the complex coupling relationship and nonlinear causal relationship between variables. At the same time, it is considered that the process of cold-rolled steel has typical full-flow process characteristics and the graph attention network makes it difficult to extract the path information between the central node and its higher-order neighborhood. The neural Granger causality algorithm is used to extract the latent relationship between variables, and the basic graph structure of mechanical property prediction data is constructed. Secondly, the node embedding layer is added before the graph attention network, which leverages the symmetry nature of Node2vec method by incorporating both breadth-first and depth-first exploration strategies. This ensures a balanced exploration of diverse paths in the graph, capturing not only local structures but also higher-order relationships. The combined graph attention networks are then able to effectively capture the symmetry path information between nodes and dependencies between variables. The accuracy and superiority of this method are verified by experiments in real cold-rolled steel production cases.

Improving Quality, Productivity, and Cost Aspects of a Sewing Line of Apparel Industry Using TQM Approach

Total quality management (TQM) is a methodical strategy to minimize defects through six processes including choosing the manufacturer, gathering information, identifying the issues, analyzing the current situation, and coming up with solutions, putting the plan into action, data collection, and result analysis. The study investigates how quality, productivity, and cost aspects of a sewing line can be improved by implementing (TQM) approach in an apparel manufacturing industry in Bangladesh. This research concentrates on reducing four primary types of faults in the sewing department of DMC Apparels Ltd., such as uncut thread, up-down, broken stitch, and joint stitch. Proper information on several stitching errors was provided by the operators and helpers and those are used to assess the study in the next step. Performing the Pareto analysis and histograms to identify the primary concerns are part of the analyzing process. Moreover, using the 10 TQM pillars, the implementation step entails establishing the TQM mindset in the sewing line of the apparel industry. Several data-gathering methods are utilized to analyze primary data throughout the study’s final phase. To analyze the acquired data, Microsoft Excel was employed. The percentage of defect per hundred unit was decreased by 1.51% after optimization, as the recommended solutions’ impact on the defect level in the section was found to be quite significant. Significant parameters such as efficiency, quality, and cost aspect were analyzed and showed positive changes after implementing the TQM approach. The new technical layout also allows for the saving of five employees and a 3,000-min labor expense reduction. Finally, the research was completed by analyzing the basic pitch time graph and calculating the overall equipment effectiveness.