Set Of Graphs Research Articles

Cross-community affinity: A polarization measure for multi-community networks

This article introduces a heterophily-based metric for assessing polarization in social networks when different opposing ideological communities coexist. The proposed metric measures polarization at the node level and is based on a node’s affinity for other communities. Node-level values can then be aggregated at the community, network, or any intermediate level, resulting in a more comprehensive map of polarization. We looked at our metric on the Polblogs network, the White Helmets Twitter interaction network with two communities, and the VoterFraud2020 domain network with five communities. Additionally, we evaluated our metric on different sets of synthetic graphs to confirm that it yields low polarization scores, as expected. We employed three ways to build synthetic networks: synthetic labeling, dK-series, and network models, in order to assess how the proposed measure behaves to various topologies and network features. Then, we compared our metric to two commonly used polarization metrics, Guerra’s boundary polarization and the random walk controversy score. We also examined how our suggested metric correlates with two network metrics: assortativity and modularity.

New Binary Adducts of Panobinostat with Different Carboxylic Acid Based NSAIDs: Structural Analysis and Physicochemical Properties Investigation

AbstractAdoption of multitarget, cost‐effective fixed‐dose medication combinations can help lower the pill load without increasing the risk of adverse events. In this study, three new 1:1 drug‐drug binary solid forms of panobinostat (PNB) and nonsteroidal anti‐inflammatory drugs (NSAIDs) were effectively synthesized by liquid‐assisted grinding and slow evaporation crystallization techniques. The obtained solid forms were extensively characterized by various analytical techniques. The structural investigation revealed that all molecular adducts formed salt with a comparable (10) graph set pattern created by heteromeric interactions formed between PNB and corresponding salt formers. To determine the dissolving behavior of the newly developed adducts, solubility tests were performed at various pH levels (pH 1.2 and pH 7), and the results indicated that the solubility of all forms is increased at pH 7.0, particularly PNB.NIF has a solubility of 0.195 mg/mL, which is seven times higher than the parent drug. Furthermore, PXRD was used to assess the stability of the synthesized adduct at varied temperature and humidity levels and it was found that all the adducts are stable. Based on the findings, we hope that the newly found PNB drug‐drug binary adducts have possible potential to broaden the use of drug combinations without changing the chemical structures.

Zero Forcing Domination in Some Graphs: Characterizations and Derived Formulas

In this paper, we initiate the study on zero forcing domination in a graph and we characterize the zero forcing dominating sets in some special graphs and the join of two graphs. We derive some formulas of the parameter using characterization results. Moreover, we present some relationships of this parameter with other known parameters in graph theory.

Efficient identification of maximum independent sets in stochastic multilayer graphs with learning automata

Investigating the maximum independent set in stochastic multilayer graphs provides critical insights into the structural and dynamical properties of complex networks. Recently, stochastic multilayer graphs effectively model the intricate interactions and interdependencies inherent in real-world systems, including social, biological, and transportation networks. The identification of a maximum independent set -comprising nodes without direct connections- offers a significant understanding of phenomena such as information diffusion, resource allocation, and epidemic spread within complex social networks. For instance, independent sets play a crucial role in identifying influencers -individuals who profoundly impact their peers, propagating information or opinions widely. In this paper, we introduce the stochastic version of the maximum independent set and propose five algorithms based on learning automata to identify maximum independent sets in the stochastic multilayer graphs. Our approach utilizes learning automata to provide a guided sampling from candidate independent sets of the stochastic multilayer graph, aiming to identify the independent set with the maximum expected value while utilizing fewer vertex samples than standard methods that do not incorporate the learning. In addition to proving several mathematical properties of the proposed approach, simulations conducted across diverse stochastic multilayer graphs demonstrate that our learning automata-based algorithms outperform traditional approaches, achieving higher convergence rates and requiring fewer samples.

Fault-tolerant metric dimension of the intersection graph of gamma sets in the zero-divisor graph

Fault-tolerant metric dimension of the intersection graph of gamma sets in the zero-divisor graph

State of the Art and Potentialities of Graph-level Learning

Graphs have a superior ability to represent relational data, such as chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks, including comparison, regression, classification, and more. Traditional approaches to learning a set of graphs heavily rely on hand-crafted features, such as substructures. While these methods benefit from good interpretability, they often suffer from computational bottlenecks, as they cannot skirt the graph isomorphism problem. Conversely, deep learning has helped graph-level learning adapt to the growing scale of graphs by extracting features automatically and encoding graphs into low-dimensional representations. As a result, these deep graph learning methods have been responsible for many successes. Yet, no comprehensive survey reviews graph-level learning starting with traditional learning and moving through to the deep learning approaches. This article fills this gap and frames the representative algorithms into a systematic taxonomy covering traditional learning, graph-level deep neural networks, graph-level graph neural networks, and graph pooling. In addition, the evolution and interaction between methods from these four branches within their developments are examined to provide an in-depth analysis. This is followed by a brief review of the benchmark datasets, evaluation metrics, and common downstream applications. Finally, the survey concludes with an in-depth discussion of 12 current and future directions in this booming field.

On Study of Some Bounds for Fault-Tolerant Metric Dimension and Adjacency Fault-Tolerant Resolving Set of Corona Product Graphs

On Study of Some Bounds for Fault-Tolerant Metric Dimension and Adjacency Fault-Tolerant Resolving Set of Corona Product Graphs

On regular sets in Cayley sum graphs

On regular sets in Cayley sum graphs

The number of independent sets in bipartite graphs and benzenoids

The number of independent sets in bipartite graphs and benzenoids

GCFExplainer: Global Counterfactual Explainer for Graph Neural Networks

Graph neural networks (GNNs) find applications in various domains such as computational biology, natural language processing, and computer security. Owing to their popularity, there is an increasing need to explain GNN predictions since GNNs are black-box machine learning models. One way to address this issue involves using counterfactual reasoning where the objective is to alter the GNN prediction by minimal changes in the input graph. Existing methods for counterfactual explanation of GNNs are limited to instance-specific local reasoning. This approach has two major limitations of not being able to offer global recourse policies and overloading human cognitive ability with too much information. In this work, we study the global explainability of GNNs through global counterfactual reasoning. Specifically, we want to find a small set of representative counterfactual graphs that explains all input graphs. Towards this goal, we propose GCF Explainer , a novel algorithm powered by vertex-reinforced random walks on an edit map of graphs with a greedy summary . Extensive experiments on real graph datasets show that the global explanation from GCF Explainer provides important high-level insights of the model behavior and achieves a 46.9% gain in recourse coverage, a 9.5% reduction in recourse cost compared to the state-of-the-art local counterfactual explainers. We also demonstrate that GCF Explainer generates explanations that are more consistent with input dataset characteristics, and is robust under adversarial attacks. In addition, K-GCF Explainer , which incorporates a graph clustering component into GCF Explainer , is introduced as a more competitive extension for datasets with a clustering structure, leading to superior performance in three out of four datasets in the experiments and better scalability.

A novel graph convolutional network-based interpretable method for chiller energy consumption prediction considering the spatiotemporal coupling between variables

The prediction of chiller energy consumption is critical for lowering the building’s energy consumption. Deep neural networks have been widely applied in this field. However, traditional deep learning methods only consider operational data and do not incorporate empirical knowledge and working condition information that are beneficial for chiller energy consumption prediction. The graph convolutional network (GCN) can handle this problem well, as it is able to incorporate empirical knowledge and working condition information into the network. However, it is important to avoid the excessive influence of empirical knowledge and working condition information on the model’s accuracy. To adjust the weight of the influence of the association graph and training set on model accuracy in the GCN network, a coefficient θ was introduced. Herein, a novel GCN (θ-GCN)-based method for the energy consumption prediction of chillers is proposed. This proposed method first combines empirical knowledge and working condition information to obtain the adjacency matrix among operational data and then constructs an association graph based on this adjacency matrix. Secondly, due to the temporal correlation of the collected dataset, a gated recurrent unit (GRU) is used for feature extraction. Lastly, the features extracted through GRU are input into the constructed association graph, and the θ-GCN network is used for training and energy consumption prediction. The proposed method was experimentally verified in an actual chiller system and compared with existing methods; the outcomes indicated that the established method could obtain better prediction accuracy.

PBIB-Designs Arising From BI-Connected Dominating Sets of Cubic Graphs of Order at Most 12

A $(v, b, \gamma_{bc}, r, \lambda_{i})$-design over regular graph $G = (V, E)$ of degree $k$ is an ordered pair $D = (V, B)$, where $|V| = v$ and $B$ is the set of bi-connected dominating sets of $G$ called blocks such that two vertices $\alpha$ and $\beta$ which are $i^{th}$ associates occur together in $ \lambda_{i}$ blocks, the numbers $\lambda_{i}$ being independent of the choice of the pair $\alpha$ and $\beta$. In this paper, we obtain Partially Balanced Incomplete Block (PBIB)-designs arising from bi-connected dominating sets in cubic graphs. Also, we give a complete list of PBIB-designs with respect to the bi-connected dominating sets for cubic graphs of order at most $12$. The discussion of non-existence of some designs corresponding to bi-connected dominating sets from certain graphs concludes the article.

2-Bromo-acetamide.

The title compound, C2H4BrNO, crystallizes in the monoclinic space group P21/c with one mol-ecule in the asymmetric unit. The almost planar mol-ecules are organized via N-H⋯O hydrogen bonds into a ladder-type network, which can be characterized by the graph sets R 2 2(8) and R 2 4(8). In addition, the mol-ecules are connected by C-H⋯O and C-H⋯Br contacts.

HATZFS predicts pancreatic cancer driver biomarkers by hierarchical reinforcement learning and zero-forcing set

The search for cancer biomarkers is of great significance for the early diagnosis and clinical treatment planning of pancreatic cancer. RNA transcription networks can effectively represent the interactions between RNA molecules, and the irregular perturbations in these interactions can lead to pathological states, making them commonly used for identifying cancer biomarkers. However, traditional network-based methods for identifying cancer biomarkers often rely on prior information and mutation data. Furthermore, most network controllability-based methods face the limitation of high computational complexity, preventing their integration with deep learning methods. In this paper, we propose a novel deep learning framework, called HATZFS, for identifying driver biomarkers in pancreatic cancer using RNA differential expression data. The proposed model combines hierarchical deep Q-network (HDQN), graph attention network (GAT), and zero-forcing set (ZFS). Firstly, a pancreatic cancer RNA transcription regulatory network is constructed to embed the complex relationship among Long non-coding RNA (lncRNA), microRNA (miRNA) and messenger RNA (mRNA). Then, we transform it into multiple subgraphs using graph sampling method, and apply GAT to learn the node features of the subgraphs. Finally, the HATZFS performs HDQN to select subgraphs and identify important RNA as driver nodes, and determining the controllability of the subgraphs based on ZFS. More important, the paper theoretically proves that when all subgraphs are controllable, the original graph is also controllable, and the union of the driver node sets of all subgraphs is equal to the driver node set of the original graph. To confirm the effectiveness of the proposed model, comprehensive experiments are conducted on the benchmark dataset consisting of 14 databases, comparing it with eight other algorithms. The experimental results demonstrate that the proposed model outperforms other methods. Overall, HATZFS not only provides the importance of all RNA molecules in the pancreatic cancer RNA regulatory network, but also identifies the driver node set of the network as driver biomarkers. Source code can be accessed at https://github.com/HongJieTongXue/HATZFS.

Edge open packing: Complexity, algorithmic aspects, and bounds

Given a graph G, two edges e1,e2∈E(G) are said to have a common edge e≠e1,e2 if e joins an endvertex of e1 to an endvertex of e2. A subset B⊆E(G) is an edge open packing set in G if no two edges of B have a common edge in G, and the maximum cardinality of such a set in G is called the edge open packing number, ρeo(G), of G. In this paper, we prove that the decision version of the edge open packing number is NP-complete even when restricted to graphs with universal vertices, Eulerian bipartite graphs, and planar graphs with maximum degree 4, respectively. In contrast, we present a linear-time algorithm that computes the edge open packing number of a tree. We also resolve two problems posed in the seminal paper (Chelladurai et al. (2022) [5]). Notably, we characterize the graphs G that attain the upper bound ρeo(G)≤|E(G)|/δ(G), and provide lower and upper bounds for the edge-deleted subgraph of a graph and establish the corresponding realization result.

Ultimate Greedy Approximation of Independent Sets in Subcubic Graphs

Ultimate Greedy Approximation of Independent Sets in Subcubic Graphs

Connected Dominating Set Construction Using the Hunger Games Search Optimisation Algorithm in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) play a significant role in monitoring changes in the physical environment, relying on a subset of designated nodes known as the Connected Dominating Set (CDS) to facilitate communication and serve as the network's virtual backbone for routing and clustering. Despite the various algorithms for CDS construction, the challenges persist in terms of construction cost and scalability. In this context, this paper introduces the utilisation of the Hunger Games Search Optimisation Algorithm (HGSOA) for Connected Dominating Set Construction in Wireless Sensor Networks (HGSOA-CDS-WSN). The primary intention of this paper is “to develop a technique capable of constructing small-sized CDS with reduced construction costs, particularly suitable for uniformly or randomly distributed nodes”. The proposed HGSOA-CDS-WSN method is implemented in MATLAB based on various metrics. The results are compared with those of existing techniques, such as the Parallel Structure from Motion for UAV Pictures using Weighted CDS (PSfM-CDS-WSN), Polyhedra Associated with Locating-Dominating, Open Locating-Dominating, and Locating Total-Dominating Sets in Graphs (PAL-CDS-WSN), and Sustainable Maintenance of Connected Dominating Set by Solar Energy Harvesting for Internet of Things Networks (SHE-CDS-WSN). The proposed technique achieves lower delay by 13.24%, 25.64%, and 9.96%, and higher throughput by 18.34%, 24.55%, and 23.04% compared to the existing methods. This systematic evaluation underscores the efficacy and superiority of the proposed HGSOA-CDS-WSN technique in terms of connected dominating set size, construction time, energy efficiency, network stability, and overall performance, highlighting its potential to advance wireless sensor network applications.

Visualization and Analysis of Three-Way Data Using Accumulated Concept Graphs

This paper introduces the Accumulated Concept Graph (ACG), a visualization tool based on the quantile method designed to analyze three-way data, including distributional data. Such data often have complex structures that make it difficult to identify patterns using conventional visualization techniques. The ACG represents each object with one or more monotonic line graphs. As a result, the three-way data are visualized as a set of parallel monotonic line graphs that never intersect. This non-intersecting property allows for the easy identification of both macroscopic and microscopic patterns within the data. We demonstrate the usefulness of ACGs and principal component analysis in the analysis of real three-way datasets.

The analysis of traveling wave solutions and dynamical behavior for the stochastic coupled Maccari's system via Brownian motion

The stochastic coupled Maccari's system (MS) is a kind of important nonlinear partial differential equations to describe fluid flow, plasma physics, nonlinear optics and so on. In this article, the dynamical behavior and some new exact traveling wave solutions of the system are investigated. By means of complex traveling wave transformation, the system is transformed into a nonlinear ordinary differential equation. The dynamical behavior of the system as well as its perturbation case are illustrated by bifurcation theory. And then, some new stochastic traveling wave solutions of the system are extracted based on the theory of polynomial complete discrimination system. To show the effect of stochastic factor on the solutions, their structures under different Brownian motion amplitudes are compared by several sets of graphs. The results obtained in this paper have supplemented the study of the system, and the technique used to exploit the traveling wave solutions are effective.

Deep spatio-temporal feature fusion learning for multi-step building cooling load forecasting

Accurate forecasting of building cooling load is essential for optimizing control strategies and energy efficiency in heating, ventilation, and air conditioning (HVAC) systems. However, existing machine learning and deep learning algorithms encounter challenges in addressing the dynamics and uncertain nature of cooling load demand, as they solely focus on temporal analysis. To tackle this issue, the paper proposes CRG-Informer, a deep learning approach that integrates spatio-temporal features to enhance multi-step predictive performance. Firstly, a time series spatial control relationship graph set is constructed based on the interconnected structure, static attributes, and control characteristics of the cooling system. Then, a graph neural network (GNN) is designed for graph embedding to extract spatial correlation information at each instance. Additionally, the Informer model with the ProbSparse self-attention mechanism is utilized to capture long-term temporal dependencies among input sequences. This integration of components enables feature fusion, and the proposed approach is evaluated using data from an office building in Hangzhou, China, over an entire cooling season. Extensive experiments were conducted to compare our method with five superior baseline models for 6, 12, 24, 72, and 144-step cooling load forecasting across four types of data acquisition intervals. The results demonstrate that the CRG-Informer, through spatio-temporal feature fusion, outperforms existing methods and provides a novel solution for improving cooling load forecasting performance.