Search Results (1,092)

The $N_k$-index (k-distance degree index) of a connected graph G was first introduced by Naji and Soner as a generalization of the distance degree concept, as $N_k\left(G\right)={\displaystyle \sum _{k=1}^{d\left(G\right)}}\left({\displaystyle \sum _{v\in V\left(G\right)}}{d}_k\left(v\right)\right)k$, where the distance between u and v in G is denoted by $d(u,v)$, the diameter of a graph G is denoted by $d\left(G\right)$, and the degree of a vertex v at distance k is denoted by $d_k\left(v\right)=\{u,v\in V\left(G\right)d(u,v)=k\}$. In this paper, we extend the study of the $N_k$-index of graphs. We introduced some graph transformations and their impact on the $N_k$-index of graph and proved that the star graph has the minimum, and the path graph has the maximum $N_k$-index among the set of all trees on n vertices. We also show that among all trees with fixed maximum-degree $\Delta$, the broom graph $B_{n,\Delta }$ (consisting of a star $S_{\Delta +1}$ and a pendant path of length $n-\Delta -1$ attached to any arbitrary pendant path of star) is a unique tree which maximizes the $N_k$-index. Further, we also defined and proved a graph with maximum $N_k$-index for a given number of n vertices, maximum-degree $\Delta$, and perfect matching among trees. We characterize the starlike trees which minimize the $N_k$-index and propose a unique tree which minimizes the $N_k$-index with diameter d and n vertices among trees. Full article

The rapid development of information technology has made cyberspace security an increasingly critical issue. Network intrusion detection methods are practical approaches to protecting network systems from cyber attacks. However, cyberspace security threats have topological dependencies and fine-grained attack semantics. Existing graph-based approaches either underestimate edge-level features or fail to balance detection accuracy with adversarial robustness. To handle these problems, we propose a novel graph neural network–based method for network intrusion detection called the adversarial hierarchical-aware edge attention learning method (AH-EAT). It leverages the natural graph structure of computer networks to achieve robust, multi-grained intrusion detection. Specifically, AH-EAT includes three main modules: an edge-based graph attention embedding module, a hierarchical multi-grained detection module, and an adversarial training module. In the first module, we apply graph attention networks to aggregate node and edge features according to their importance. This effectively captures the network’s key topological information. In the second module, we first perform coarse-grained detection to distinguish malicious flows from benign ones, and then perform fine-grained classification to identify specific attack types. In the third module, we use projected gradient descent to generate adversarial perturbations on network flow features during training, enhancing the model’s robustness to evasion attacks. Experimental results on four benchmark intrusion detection datasets show that AH-EAT achieves 90.73% average coarse-grained accuracy and 1.45% ASR on CIC-IDS2018 under adversarial attacks, outperforming state-of-the-art methods in both detection accuracy and robustness. Full article

Urban plots are pivotal links between individual buildings and the city fabric, yet conventional plot classification methods often overlook how buildings interact within each plot. This oversight is particularly problematic in the irregular fabrics typical of many Global South cities. This study aims to create a plot classification method that jointly captures metric and configurational characteristics. Our approach converts each cadastral plot into a graph whose nodes are building centroids and whose edges reflect Delaunay-based proximity. The model then learns unsupervised graph embeddings with a two-layer Graph Attention Network guided by a triple loss that couples building morphology with spatial topology. We then cluster the embeddings together with normalized plot metrics. Applying the model to 8973 plots in Nanjing’s historic walled city yields seven distinct plot morphological types. The framework separates plots that share identical FAR–GSI values but differ in internal organization. The baseline and ablation experiments confirm the indispensability of both configurational and metric information. Each type aligns with specific renewal strategies, from incremental upgrades of courtyard slabs to skyline management of high-rise complexes. By integrating quantitative graph learning with classical typo-morphology theory, this study not only advances urban form research but also offers planners a tool for context-sensitive urban regeneration and land-use management. Full article

Identifying correspondences of road segments in different road networks, namely road-network matching, is an essential task for road network-centric data processing such as data integration of road networks and data quality assessment of crowd-sourced road networks. Traditional road-network matching usually relies on feature engineering and parameter selection of the geometry and topology of road networks for similarity measurement, resulting in poor performance when dealing with dense and irregular road network structures. Recent development of graph neural networks (GNNs) has demonstrated unsupervised modeling power on road network data, which learn the embedded vector representation of road networks through spatial feature induction and topology-based neighbor aggregation. However, weighting spatial information on the node feature alone fails to give full play to the expressive power of GNNs. To this end, this paper proposes a Spatial Pattern-aware Graph EMbedding learning method for road-network matching, named SP-GEM, which explores the idea of spatially-explicit modeling by identifying spatial patterns in neighbor aggregation. Firstly, a road graph is constructed from the road network data, and geometric, topological features are extracted as node features of the road graph. Then, four spatial patterns, including grid, high branching degree, irregular grid, and circuitous, are modelled in a sector-based road neighborhood for road embedding. Finally, the similarity of road embedding is used to find data correspondences between road networks. We conduct an algorithmic accuracy test to verify the effectiveness of SP-GEM on OSM and Tele Atlas data. The algorithmic accuracy experiments show that SP-GEM improves the matching accuracy and recall by at least 6.7% and 10.2% among the baselines, with high matching success rate (>70%), and improves the matching accuracy and recall by at least 17.7% and 17.0%, compared to the baseline GNNs, without spatially-explicit modeling. Further embedding analysis also verifies the effectiveness of the induction of spatial patterns. This study not only provides an effective and practical algorithm for road-network matching, but also serves as a test bed in exploring the role of spatially-explicit modeling in GNN-based road network modeling. The experimental performances of SP-GEM illuminate the path to develop GeoEmbedding services for geospatial applications. Full article

This study introduces a new metric structure called the Graphical Fuzzy Cone Metric Space (GFCMS) and explores its essential properties in detail. We examine its topological aspects in detail and introduce the notion of Hausdorff distance within this setting—an advancement not previously explored in any graphical structure. Furthermore, a fixed-point result is proven within the framework of GFCMS, accompanied by examples that demonstrate the applicability of the theoretical results. As a significant application, we construct fractals within GFCMS, marking the first instance of fractal generation in a graphical structure. This pioneering work opens new avenues for research in graph theory, fuzzy metric spaces, topology, and fractal geometry, with promising implications for diverse scientific and computational domains. Full article

Consensus protocols for a multi-agent networked system consist of strategies that align the states of all agents that share information according to a given network topology, despite challenges such as communication limitations, time-varying networks, and communication delays. The special orthogonal group $SO\left(n\right)$ plays a key role in applications from rigid body attitude synchronization to machine learning on Lie groups, particularly in fields like physics-informed learning and geometric deep learning. In this paper, N-agent consensus protocols are proposed on the Lie group $SO\left(4\right)$ and the corresponding tangent bundle $TSO\left(4\right)$, in which the state spaces are $SO{\left(4\right)}^N$ and $TSO{\left(4\right)}^N$, respectively. In particular, when using communication topologies such as a ring graph for which the local stability of non-consensus equilibria is retained in the closed loop, a consensus protocol that leverages a reshaping strategy is proposed to destabilize non-consensus equilibria and produce consensus with almost global stability on $SO{\left(4\right)}^N$ or $TSO{\left(4\right)}^N$. Lyapunov-based stability guarantees are obtained, and simulations are conducted to illustrate the advantages of these proposed consensus protocols. Full article

Construction projects still face persistent barriers to adopting whole life costing (WLC), such as fragmented data, a lack of standardization, and inadequate tools. This study addresses these limitations by proposing a core ontology for WLC, developed using an ontology design science research methodology. The ontology formalizes WLC knowledge based on ISO 15686-5 and incorporates professional insights from surveys and expert focus groups. Implemented in web ontology language (OWL), it models cost categories, temporal aspects, and discounting logic in a machine-interpretable format. The ontology’s interoperability and extensibility are validated through its integration with the building topology ontology (BOT). Results show that the ontology effectively supports cost breakdown, time-based projections, and calculation of discounted values, offering a reusable structure for different project contexts. Practical validation was conducted using SQWRL queries and Python scripts for cost computation. The solution enables structured data integration and can support decision-making throughout the building life cycle. This work lays the foundation for future semantic web applications such as knowledge graphs, bridging the current technological gap and facilitating more informed and collaborative use of WLC in construction. Full article

This entry gives an overview of the main data structures and approaches used for a two-dimensional representation of the terrain surface using a digital elevation model (DEM). A DEM represents the elevation of the earth surface from a set of points. It is used for terrain analysis, visualisation and interpretation. DEMs are most commonly defined as a grid where an elevation is assigned to each grid cell. Due to its simplicity, the square grid structure is the most common DEM structure. However, it is less adaptive and shows limitations for more complex processing and reasoning. Hence, the triangulated irregular network is a more adaptive structure and explicitly stores the relationships between the points. Other topological structures (contour graphs, contour trees) have been developed to study terrain morphology. Topological relationships are captured in another structure, the surface network (SN), composed of critical points (peaks, pits, saddles) and critical lines (thalweg, ridge lines). The SN can be computed using either a TIN or a grid. The Morse Theory provides a mathematical approach to studying the topology of surfaces, which is applied to the SN. It has been used for terrain simplification, multi-resolution modelling, terrain segmentation and landform identification. The extended surface network (ESN) extends the classical SN by integrating both the surface and the drainage networks. The ESN can itself be extended for the cognitive representation of the terrain based on saliences (typical points, lines and regions) and skeleton lines (linking critical points), while capturing the context of the appearance of landforms using topo-contexts. Full article

The proliferation of malicious social bots poses severe threats to cybersecurity and social media information ecosystems. Existing detection methods often overlook the semantic value and emotional cues conveyed by emojis in user-generated tweets. To address this gap, we propose ESA-BotRGCN, an emoji-driven multi-modal detection framework that integrates semantic enhancement, sentiment analysis, and multi-dimensional feature modeling. Specifically, we first establish emoji–text mapping relationships using the Emoji Library, leverage GPT-4 to improve textual coherence, and generate tweet embeddings via RoBERTa. Subsequently, seven sentiment-based features are extracted to quantify statistical disparities in emotional expression patterns between bot and human accounts. An attention gating mechanism is further designed to dynamically fuse these sentiment features with user description, tweet content, numerical attributes, and categorical features. Finally, a Relational Graph Convolutional Network (RGCN) is employed to model heterogeneous social topology for robust bot detection. Experimental results on the TwiBot-20 benchmark dataset demonstrate that our method achieves a superior accuracy of 87.46%, significantly outperforming baseline models and validating the effectiveness of emoji-driven semantic and sentiment enhancement strategies. Full article

The Bayesian network is a directed, acyclic graphical model that can offer a structured description for probabilistic dependencies among random variables. As powerful tools for classification tasks, Bayesian classifiers often require computing joint probability distributions, which can be computationally intractable due to potential full dependencies among feature variables. On the other hand, Naïve Bayes, which presumes zero dependencies among features, trades accuracy for efficiency and often comes with underperformance. As a result, non-zero dependency structures, such as trees, are often used as more feasible probabilistic graph approximations; in particular, Tree Augmented Naïve Bayes (TAN) has been demonstrated to outperform Naïve Bayes and has become a popular choice. For applications where a variable is strongly influenced by multiple other features, TAN has been further extended to the k-dependency Bayesian classifier (KDB), where one feature can depend on up to k other features (for a given $k\ge 2$). In such cases, however, the selection of the k parent features for each variable is often made through heuristic search methods (such as sorting), which do not guarantee an optimal approximation of network topology. In this paper, the novel notion of k-tree Augmented Naïve Bayes (k-TAN) is introduced to augment Naïve Bayesian classifiers with k-tree topology as an approximation of Bayesian networks. It is proved that, under the Kullback–Leibler divergence measurement, k-tree topology approximation of Bayesian classifiers loses the minimum information with the topology of a maximum spanning k-tree, where the edge weights of the graph are mutual information between random variables conditional upon the class label. In addition, while in general finding a maximum spanning k-tree is NP-hard for fixed $k\ge 2$, this work shows that the approximation problem can be solved in time $O\left(n^{k+1}\right)$ if the spanning k-tree also desires to retain a given Hamiltonian path in the graph. Therefore, this algorithm can be employed to ensure efficient approximation of Bayesian networks with k-tree augmented Naïve Bayesian classifiers of the guaranteed minimum loss of information. Full article

This paper introduces a framework of hypercompositional algebra on fuzzy graphs by defining and analyzing fuzzy path-based hyperoperations. Building on the notion of strongest strong paths (paths that are both strength-optimal and composed exclusively of strong edges, where each edge achieves maximum connection strength between its endpoints), we define two operations: a vertex-based fuzzy path hyperoperation and an edge-based variant. These operations generalize classical graph hyperoperations to the fuzzy setting while maintaining compatibility with the underlying topology. We prove that the vertex fuzzy path hyperoperation is associative, forming a fuzzy hypersemigroup, and establish additional properties such as reflexivity and monotonicity with respect to $\alpha$-cuts. Structural features such as fuzzy strong cut vertices and edges are examined, and a fuzzy distance function is introduced to quantify directional connectivity strength. We define an equivalence relation based on mutual full-strength reachability and construct a quotient fuzzy graph that reflects maximal closed substructures under the vertex fuzzy path hyperoperation. Applications are discussed in domains such as trust networks, biological systems, and uncertainty-aware communications. This work aims to lay the algebraic foundations for further exploration of fuzzy hyperstructures that support modeling, analysis, and decision-making in systems governed by partial and asymmetric relationships. Full article

LiDAR point clouds, as direct carriers of 3D spatial information, comprehensively record the geometric features and spatial topological relationships of object surfaces, providing intelligent systems with rich 3D scene representation capability. However, current point cloud semantic segmentation methods primarily extract features through operations such as convolution and pooling, yet fail to adequately consider sparse features that significantly influence the final results of point cloud-based scene perception, resulting in insufficient feature representation capability. To address these problems, a sparse feature dynamic graph convolutional neural network, abbreviated as SFDGNet, is constructed in this paper for LiDAR point clouds of complex scenes. In the context of this paper, sparse features refer to feature representations in which only a small number of activation units or channels exhibit significant responses during the forward pass of the model. First, a sparse feature regularization method was used to motivate the network model to learn the sparsified feature weight matrix. Next, a split edge convolution module, abbreviated as SEConv, was designed to extract the local features of the point cloud from multiple neighborhoods by dividing the input feature channels, and to effectively learn sparse features to avoid feature redundancy. Finally, a multi-neighborhood feature fusion strategy was developed that combines the attention mechanism to fuse the local features of different neighborhoods and obtain global features with fine-grained information. Taking S3DIS and ScanNet v2 datasets, we evaluated the feasibility and effectiveness of SFDGNet by comparing it with six typical semantic segmentation models. Compared with the benchmark model DGCNN, SFDGNet improved overall accuracy $\left(OA\right)$, mean accuracy $\left(mAcc\right)$, mean intersection over union $\left(mIoU\right)$, and $sparsity$ by $1.8\%$, $3.7\%, 3.5\%$, and $85.5\%$ on the S3DIS dataset, respectively. The $mIoU$ on the ScanNet v2 validation set, $mIoU$ on the test set, and $sparsity$ were improved by $3.2\%, 7.0\%$, and $54.5\%$, respectively. Full article

As global urbanization accelerates, communities have emerged as key areas where social conflicts and public safety risks clash. Traditional crime prevention models experience difficulties handling dynamic crime hotspots due to data lags and poor spatiotemporal resolution. Therefore, this study proposes a hybrid model combining Informer and Spatiotemporal Graph Convolutional Network (ST-GCN) to achieve precise crime prediction at the community level. By employing a community topology and incorporating historical crime, weather, and holiday data, ST-GCN captures spatiotemporal crime trends, while Informer identifies temporal dependencies. Moreover, the model leverages a fully connected layer to map features to predicted latitudes. The experimental results from 320,000 crime records from 22 police districts in Chicago, IL, USA, from 2015 to 2020 show that our model outperforms traditional and deep learning models in predicting assaults, robberies, property damage, and thefts. Specifically, the mean average error (MAE) is 0.73 for assaults, 1.36 for theft, 1.03 for robbery, and 1.05 for criminal damage. In addition, anomalous event fluctuations are effectively captured. The results indicate that our model furthers data-driven public safety governance through spatiotemporal dependency integration and long-sequence modeling, facilitating dynamic crime hotspot prediction and resource allocation optimization. Future research should integrate multisource socioeconomic data to further enhance model adaptability and cross-regional generalization capabilities. Full article

Mineral prospectivity mapping (MPM) is a pivotal technique in geoscientific mineral resource exploration. To address three critical challenges in current deep convolutional neural network applications for geoscientific mineral resource prediction—(1) model bias induced by imbalanced distribution of ore deposit samples, (2) deficiency in global feature extraction due to excessive reliance on local spatial correlations, and (3) diminished discriminative capability caused by feature smoothing in deep networks—this study innovatively proposes a T-GCN model integrating Transformer with graph convolutional neural networks (GCNs). The model achieves breakthrough performance through three key technological innovations: firstly, constructing a global perceptual field via Transformer’s self-attention mechanism to effectively capture long-range geological relationships; secondly, combining GCNs’ advantages in topological feature extraction to realize multi-scale feature fusion; and thirdly, designing a feature enhancement module to mitigate deep network degradation. In practical application to the PangXD ore district, the T-GCN model achieved a prediction accuracy of 97.27%, representing a 3.76 percentage point improvement over the best comparative model, and successfully identified five prospective mineralization zones, demonstrating its superior performance and application value under complex geological conditions. Full article

Substitutional doping of fullerenes represents a significant category of heterofullerenes. Due to the vast number of isomers, confirming the ground state structure poses considerable challenges. In this study, we generated isomers of C_60−nB_n and C_60−nN_n with n ranging from 2 to 12. To avoid overlooking the ground state structures, we applied specific filtering rules: no adjacent nitrogen (N) or boron (B) atoms are allowed, and substitutions in meta-positions within pentagons are prohibited when the substitution number n exceeds nine. Approximately 15,000 isomers across various values of n within the range of 2 to 12 for B and N substituted fullerenes were selected and optimized using density functional theory (DFT) calculations, forming our dataset. We developed a Graph Neural Network (GNN) that aggregates both topological connections and its dual graph with ring types as input information to predict their binding energies. The GNN achieved high accuracy, reaching a root mean square error (RMSE) of 1.713 meV. Furthermore, it operates efficiently; indeed, it can predict over six thousand isomers per second on an eight-core PC. Several predicted stable structures were further optimized by DFT to confirm their ground state configurations. The energy cutoffs of each composition were determined through statistical simulations to ensure that the selected ground state structures possess high confidence levels. Notably, new lower-energy structures have been discovered for boron-substituted fullerenes with substitution number ranging from seven to twelve and nitride-substituted fullerenes with substitution number ranging from seven to eleven. Full article