Search Results (326)

Link prediction is a fundamental problem in graphs. Currently, SubGraph Representation Learning (SGRL) methods provide state-of-the-art solutions for link prediction by transforming the task into a graph classification problem. However, existing SGRL solutions suffer from high computational costs and lack scalability. In this paper, we propose a novel SGRL framework called Augmented Feature Diffusion on Sparsely Sampled Subgraph (AFD3S). The AFD3S first uses a conditional variational autoencoder to augment the local features of the input graph, effectively improving the expressive ability of downstream Graph Neural Networks. Then, based on a random walk strategy, sparsely sampled subgraphs are obtained from the target node pairs, reducing computational and storage overhead. Graph diffusion is then performed on the sampled subgraph to achieve specific weighting. Finally, the diffusion matrix of the subgraph and its augmented feature matrix are used for feature diffusion to obtain operator-level node representations as inputs for the SGRL-based link prediction. Feature diffusion effectively simulates the message-passing process, simplifying subgraph representation learning, thus accelerating the training and inference speed of subgraph learning. Our proposed AFD3S achieves optimal prediction performance on several benchmark datasets, with significantly reduced storage and computational costs. Full article

Let $n,m,p,r\in N$ with $p\ge n\ge r$. For a hypergraph, if each edge has r vertices, then the hypergraph is called an r-graph. Define $e_r(n,m;p)$ to be the maximum number of edges of an r-graph with p vertices in which every subgraph of n vertices has at most m edges. Researching this function constitutes a Turán type problem. In this paper, on the one hand, for fixed p, we present some results about the exact values of $e_r(n,m;p)$ for small m compared to n; on the other hand, for sufficient large p, we use the combinatorial technique of double counting to give an upper bound of $e(n,m;p)$ and obtain a lower bound of $e_r(n,m;p)$ by applying the lower bound of the independent set of a hypergraph. Full article

Clique counts are crucial in applications like detecting communities in social networks and recurring patterns in bioinformatics. Counting k-cliques—a fully connected subgraph with k nodes, where each node has a direct, mutual, and symmetric relationship with every other node—becomes computationally challenging for larger k due to combinatorial explosion, especially in large, dense graphs. Existing exact methods have difficulties beyond k = 10, especially on large datasets, while sampling-based approaches often involve trade-offs in terms of accuracy, resource utilization, and efficiency. This difficulty becomes more pronounced in dense graphs as the number of potential k-cliques grows exponentially. We present Boundary-driven approximations of k-cliques (BDAC), a novel algorithm that approximates k-clique counts without using recursive procedures or sampling methods. BDAC offers both lower and upper bounds for k-cliques at local (per-vertex) and global levels, making it ideal for large, dense graphs. Unlike other approaches, BDAC’s complexity remains unaffected by the value of k. We demonstrate its effectiveness by comparing it with leading algorithms across various datasets, focusing on k values ranging from 8 to 50. Full article

Studying gene regulatory networks (GRNs) is paramount for unraveling the complexities of biological processes and their associated disorders, such as diabetes, cancer, and Alzheimer’s disease. Recent advancements in computational biology have aimed to enhance the inference of GRNs from gene expression data, a non-trivial task given the networks’ intricate nature. The challenge lies in accurately identifying the myriad interactions among transcription factors and target genes, which govern cellular functions. This research introduces a cutting-edge technique, EGRC (Effective GRN Inference applying Graph Convolution with Self-Attention Graph Pooling), which innovatively conceptualizes GRN reconstruction as a graph classification problem, where the task is to discern the links within subgraphs that encapsulate pairs of nodes. By leveraging Spearman’s correlation, we generate potential subgraphs that bring nonlinear associations between transcription factors and their targets to light. We use mutual information to enhance this, capturing a broader spectrum of gene interactions. Our methodology bifurcates these subgraphs into ‘Positive’ and ‘Negative’ categories. ‘Positive’ subgraphs are those where a transcription factor and its target gene are connected, including interactions among their neighbors. ‘Negative’ subgraphs, conversely, denote pairs without a direct connection. EGRC utilizes dual graph convolution network (GCN) models that exploit node attributes from gene expression profiles and graph embedding techniques to classify these. The performance of EGRC is substantiated by comprehensive evaluations using the DREAM5 datasets. Notably, EGRC attained an AUROC of 0.856 and an AUPR of 0.841 on the E. coli dataset. In contrast, the in silico dataset achieved an AUROC of 0.5058 and an AUPR of 0.958. Furthermore, on the S. cerevisiae dataset, EGRC recorded an AUROC of 0.823 and an AUPR of 0.822. These results underscore the robustness of EGRC in accurately inferring GRNs across various organisms. The advanced performance of EGRC represents a substantial advancement in the field, promising to deepen our comprehension of the intricate biological processes and their implications in both health and disease. Full article

The precise acquisition of phenotypic parameters for individual trees in plantation forests is important for forest management and resource exploration. The use of Light-Detection and Ranging (LiDAR) technology mounted on Unmanned Aerial Vehicles (UAVs) has become a critical method for forest resource monitoring. Achieving the accurate segmentation of individual tree crowns (ITCs) from UAV LiDAR data remains a significant technical challenge, especially in broad-leaved plantations such as rubber plantations. In this study, we designed an individual tree segmentation framework applicable to dense rubber plantations with complex canopy structures. First, the feature extraction module of PointNet++ was enhanced to precisely extract understory branches. Then, a graph-based segmentation algorithm focusing on the extracted branch and trunk points was designed to segment the point cloud of the rubber plantation. During the segmentation process, a directed acyclic graph is constructed using components generated through grey image clustering in the forest. The edge weights in this graph are determined according to scores calculated using the topologies and heights of the components. Subsequently, ITC segmentation is performed by trimming the edges of the graph to obtain multiple subgraphs representing individual trees. Four different plots were selected to validate the effectiveness of our method, and the widths obtained from our segmented ITCs were compared with the field measurement. As results, the improved PointNet++ achieved an average recall of 94.6% for tree trunk detection, along with an average precision of 96.2%. The accuracy of tree-crown segmentation in the four plots achieved maximal and minimal R² values of 98.2% and 92.5%, respectively. Further comparative analysis revealed that our method outperforms traditional methods in terms of segmentation accuracy, even in rubber plantations characterized by dense canopies with indistinct boundaries. Thus, our algorithm exhibits great potential for the accurate segmentation of rubber trees, facilitating the acquisition of structural information critical to rubber plantation management. Full article

With the acceleration of urbanization, public transport networks are an important part of urban transport systems, and their robustness is critical for city operation. The objective of this study is to analyze the topological properties and robustness of an urban public transport network (UPTN) with a view to enhancing the sustainability of urbanization. In order to present the topological structure of the UPTN, the L-Space complex network modeling method is used to construct a model. Topological characteristics of the network are calculated. Based on single evaluation indices of station significance, a comprehensive evaluation index is proposed as the basis for selecting critical stations. The UPTN cascading failure model is established. Using the proportion of the maximum connected subgraph as the evaluation index, the robustness of the UPTN is analyzed using different station significance indices and deliberate attack strategies. The public transport network of Xuzhou city is selected for instance analysis. The results show that the UPTN in Xuzhou city has small-world effects and scale-free characteristics. Although the network has poor connectivity, it is a convenient means to travel for residents with many independent communities. The network’s dynamic robustness is demonstrably inferior to its static robustness due to the prevalence of cascading failure phenomena. Specifically, the failure of important stations has a wider impact on the network performance. Improving their load capacity and distributing the routes via them will help bolster the network resistance against contingencies. This study provides a scientific basis and strategic recommendations for urban planners and public transport managers to achieve a more sustainable public transport system. Full article

In this paper, three sorts of network indices for the weighted three-layered graph are studied through the methods of graph spectra theory combined with analysis methods. The concept of union of graphs are applied to design two sorts of weighted layered multi-fan composed graphs, and the accurate mathematical expressions of the network indices are obtained through the derivations of Laplacian spectra; furthermore, the asymptotic properties are also derived. We find that when the cardinalities of the vertices on a sector-edge-link tend to infinity, the indices of FONC and EMFPT are irrelevant with the number of copies of the fan-substructure based on the considered graph framework. Full article

To address the limitations of existing graph contrastive learning methods, which fail to adaptively integrate feature and topological information and struggle to efficiently capture multi-hop information, we propose an adaptive multi-view parallel graph contrastive learning framework (AMPGCL). It is an unsupervised graph representation learning method designed to generate task-agnostic node embeddings. AMPGCL constructs and encodes feature and topological views to mine feature and global topological information. To encode global topological information, we introduce an H-Transformer to decouple multi-hop neighbor aggregations, capturing global topology from node subgraphs. AMPGCL learns embedding consistency among feature, topology, and original graph encodings through a multi-view contrastive loss, generating semantically rich embeddings while avoiding information redundancy. Experiments on nine real datasets demonstrate that AMPGCL consistently outperforms thirteen state-of-the-art graph representation learning models in classification accuracy, whether in homophilous or non-homophilous graphs. Full article

Finding the densest subgraph has tremendous potential in computer vision and social network research, among other domains. In computer vision, it can demonstrate essential structures, and in social network research, it aids in identifying closely associated communities. The densest subgraph problem is finding a subgraph with maximum mean density. However, most densest subgraph-finding algorithms are based on edge-weighted graphs, where edge weights can only represent a single value dimension, whereas practical applications involve multiple dimensions. To resolve the challenge, we propose two algorithms for resolving the densest subgraph problem in a vertex-weighted graph. First, we present an exact algorithm that builds upon Goldberg’s original algorithm. Through theoretical exploration and analysis, we rigorously verify our proposed algorithm’s correctness and confirm that it can efficiently run in polynomial time O(n(n + m)log²n) is its temporal complexity. Our approach can be applied to identify closely related subgroups demonstrating the maximum average density in real-life situations. Additionally, we consistently offer an approximation algorithm that guarantees an accurate approximation ratio of 2. In conclusion, our contributions enrich theoretical foundations for addressing the densest subgraph problem. Full article

A connected graph, G, is Crossing Free-connected ($\mathcal{CF}$-connected) if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G. We conjecture that a complete tripartite graph, $K_{l,m,n}$, is $\mathcal{CF}$-connected if and only if it does not contain any of the following as a subgraph: $K_{1,2,7}$, $K_{1,3,5}$, $K_{1,4,4}$, $K_{2,2,5}$, $K_{3,3,3}$. We examine the idea that $K_{1,2,7}$, $K_{1,3,5}$, $K_{1,4,4}$, and $K_{2,2,5}$ are the first non-$\mathcal{CF}$-connected complete tripartite graphs. The $\mathcal{CF}$-connectedness of $K_{l,m,n}$ with $l,m,n\ge 3$ is dependent on the knowledge of crossing numbers of $K_{3,3,n}$. In this paper, we prove various results that support this conjecture. Full article

The heterogeneous network formed by the deployment and interconnection of various network devices (e.g., sensors) has attracted widespread attention. $P{M}_{2.5}$ forecasting on the entire industrial region throughout mainland China is an important application of heterogeneous networks, which has great significance to factory management and human health travel. In recent times, Large Language Models (LLMs) have exhibited notability in terms of time series prediction. However, existing LLMs tend to forecast nationwide industry $P{M}_{2.5}$, which encounters two issues. First, most LLM-based models use centralized training, which requires uploading large amounts of data from sensors to a central cloud. This entire transmission process can lead to security risks of data leakage. Second, LLMs fail to extract spatiotemporal correlations in the nationwide sensor network (heterogeneous network). To tackle these issues, we present a novel framework entitled Spatio-Temporal Large Language Model with Edge Computing Servers (STLLM-ECS) to securely predict nationwide industry $P{M}_{2.5}$ in China. In particular, We initially partition the entire sensor network, located in the national industrial region, into several subgraphs. Each subgraph is allocated an edge computing server (ECS) for training and inference, avoiding the security risks caused by data transmission. Additionally, a novel LLM-based approach named Spatio-Temporal Large Language Model (STLLM) is developed to extract spatiotemporal correlations and infer prediction sequences. Experimental results prove the effectiveness of our proposed model. Full article

To alleviate the tense situation of limited passenger service resources in the terminal and to achieve the matching of resource scheduling with the flight support process, the process–resource interdependent network is constructed according to its mapping relationship and the time-varying characteristics of the empirical network and network evolution conditions are analyzed. Then, node capacity, node load, and the cascading failure process are investigated, the impact of average service rate and service quality standard on queue length is considered, the node capacity model is constructed under the condition of resource capacity constraints, and the load-redistribution resource adaptive scheduling method based on cascading failure is proposed. Finally, the method’s effectiveness is verified by empirical analysis, the service efficiency is assessed using the total average service time and variance, and the network robustness is assessed using the proportion of maximum connected subgraph. The results indicate that the resource adaptive scheduling method is effective in improving service efficiency, and the average value of its measurement is smaller than that of the resource average allocation method by 0.069; in terms of the robustness improvement of the interdependent network, the phenomenon of re-failure after the load redistribution is significantly reduced. Full article

Natural disasters pose serious threats to human survival. With global warming, disaster chains related to extreme weather are becoming more common, making it increasingly urgent to understand the relationships between different types of natural disasters. However, there remains a lack of research on the frequent spatial-temporal intervals between different disaster events. In this study, we utilize textual records of natural disaster events to mine frequent spatial-temporal patterns of disasters in China. We first transform the discrete spatial-temporal disaster events into a graph structure. Due to the limit of computing power, we reduce the number of edges in the graph based on domain expertise. We then apply the GraMi frequent subgraph mining algorithm to the spatial-temporal disaster event graph, and the results reveal frequent spatial-temporal intervals between disasters and reflect the spatial-temporal changing pattern of disaster interactions. For example, the pattern of sandstorms happening after gales is mainly concentrated within 50 km and rarely happens at farther spatial distances, and the most common temporal interval is 1 day. The statistical results of this study provide data support for further understanding disaster association patterns and offer decision-making references for disaster prevention efforts. Full article

The current usage of federated learning in applications relies on the existence of servers. To address the inability to conduct federated learning for IoV (Internet of Vehicles) applications in serverless areas, a P2P (peer-to-peer) architecture for federated learning is proposed in this paper. Following node segmentation based on limited subgraph diameters, an edge aggregation mode is employed to propagate models inwardly, and a mode for propagating the model inward to the C-node (center node) while aggregating is proposed. Simultaneously, a personalized differential privacy scheme was designed under this architecture. Through experimentation and verification, the approach proposed in this paper demonstrates the combination of both security and usability. Full article

Granular computing (GrC) is a methodology for reducing the complexity of problem solving and includes two basic aspects: granulation and granular-based computing. Strongly connected components (SCCs) are a significant subgraph structure in digraphs. In this paper, two new granulation strategies were devised to improve the efficiency of computing SCCs. Firstly, four SCC correlations between the vertices were found, which can be divided into two classes. Secondly, two granulation strategies were designed based on correlations between two classes of SCCs. Thirdly, according to the characteristics of the granulation results, the parallelization of computing SCCs was realized. Finally, a parallel algorithm based on granulation strategy for computing SCCs of simple digraphs named GPSCC was proposed. Experimental results show that GPSCC performs with higher computational efficiency than algorithms. Full article