Edge Weights Research Articles

Online Euclidean Spanners

In this article, we study the online Euclidean spanners problem for points in \(\mathbb{R}^{d}\) . Given a set \(S\) of \(n\) points in \(\mathbb{R}^{d}\) , a \(t\) -spanner on \(S\) is a subgraph of the underlying complete graph \(G=(S,\binom{S}{2})\) , that preserves the pairwise Euclidean distances between points in \(S\) to within a factor of \(t\) , that is the stretch factor . Suppose we are given a sequence of \(n\) points \((s_{1},s_{2},\ldots,s_{n})\) in \(\mathbb{R}^{d}\) , where point \(s_{i}\) is presented in step \(i\) for \(i=1,\ldots,n\) . The objective of an online algorithm is to maintain a geometric \(t\) -spanner on \(S_{i}=\{s_{1},\ldots,s_{i}\}\) for each step \(i\) . The algorithm is allowed to add new edges to the spanner when a new point is presented but cannot remove any edge from the spanner. The performance of an online algorithm is measured by its competitive ratio, which is the supremum, over all sequences of points, of the ratio between the weight of the spanner constructed by the algorithm and the weight of an optimum spanner. Here, the weight of a spanner is the sum of all edge weights. First, we establish a lower bound of \(\Omega(\varepsilon^{-1}\log n/\log\varepsilon^{-1})\) for the competitive ratio of any online \((1+\varepsilon)\) -spanner algorithm, for a sequence of \(n\) points in 1-dimension. We show that this bound is tight, and there is an online algorithm that can maintain a \((1+\varepsilon)\) -spanner with competitive ratio \(O(\varepsilon^{-1}\log n/\log\varepsilon^{-1})\) . Next, we design online algorithms for sequences of points in \(\mathbb{R}^{d}\) , for any constant \(d\geq 2\) , under the \(L_{2}\) norm. We show that previously known incremental algorithms achieve a competitive ratio \(O(\varepsilon^{-(d+1)}\log n)\) . However, if the algorithm is allowed to use additional points (Steiner points), then it is possible to substantially improve the competitive ratio in terms of \(\varepsilon\) . We describe an online Steiner \((1+\varepsilon)\) -spanner algorithm with competitive ratio \(O(\varepsilon^{(1-d)/2}\log n)\) . As a counterpart, we show that the dependence on \(n\) cannot be eliminated in dimensions \(d\geq 2\) . In particular, we prove that any online spanner algorithm for a sequence of \(n\) points in \(\mathbb{R}^{d}\) under the \(L_{2}\) norm has competitive ratio \(\Omega(f(n))\) , where \(\lim_{n\rightarrow\infty}f(n)=\infty\) . Finally, we provide improved lower bounds under the \(L_{1}\) norm: \(\Omega(\varepsilon^{-2}/\log\varepsilon^{-1})\) in the plane and \(\Omega(\varepsilon^{-d})\) in \(\mathbb{R}^{d}\) for \(d\geq 3\) .

A complex network analysis of groundwater wells in and around the Doñana Natural Space, Spain

This paper proposes the use of Complex Network Analysis tools to study the spatial distribution and temporal evolution of groundwater abstraction wells within a region of interest. To that end a weighted undirected network connecting wells within a certain distance was built. The edge weights take into account the distance between the wells as well as their corresponding abstraction volumes. In addition to the conventional complex network metrics, two specific abstraction-based centrality indexes are proposed, based on the total impact of a groundwater abstraction well on its surrounding wells and on the total impact of surrounding wells on a specific location. The proposed approach has been applied to the area of the Doñana Natural Space, one of the most important wetlands in Europe. The topology of the network reveals a large number of small, disconnected components and a few large components. This is reflected also in the degree distribution, which follows a Power Law distribution. The network has a large average clustering coefficient, a small average path length and a low level of centralisation. Global and average local network efficiency are also high. The network is assortative in terms of degree-degree and strength-strength correlations. Eigenvector centrality of the nodes reveals the location of influential wells.

Edge computing task scheduling method based on user’s social relations: a construction and solution for Smart City Library

In the realm of the development of a Smart City Library, the integration of robust edge computing is vital. The research suggests a novel task-scheduling model for edge computing, leveraging user’s social relationships. Analyzing these connections involves constructing a user’s social relationship graph by implementing mathematical convolution and the Jaccard similarity ratio. This precise quantification of social ties ensures secure and reliable task scheduling. An equipment connection graph of a user equipment service is also crafted based on Euclidean distance, aligning task scheduling with device-to-device (D2D) communication conditions. Combining a user’s social relationship graph and a user’s device-service device connection graph creates a task-device bipartite graph. On the other hand, the calculation of a task execution cost and edge weight determination finalize a scheduling model. Implementing the proposed method for constructing a model for edge computing task scheduling based on utilizing the Kuhn–Munkres (KM) algorithm demonstrates positive impacts, which are few delays and less energy consumption, on edge computing task scheduling. For instance, when the social threshold score changes from 02. To 0.6, the total task execution delay time increases from 23 to 32, which is the best when compared with other algorithms. The approach strengthens security and reliability while decreasing task execution delays and energy consumption. This research advances edge computing for Smart City Libraries, promising transformative implications.

Research on construction method of command and control network model based on complex network theory

AbstractThe command and control (C2) network is a complete organizational system that connects operational units at all levels based on command relationships. Its purpose is to ensure that the C2 system can fully perform its command functions, achieving high precision and efficiency in decision‐making. As warfare models evolve rapidly from network‐centric warfare to multi‐domain operations, traditional C2 networks, which utilize a tree structure for connectivity, exhibit only a single hierarchical relationship, making it challenging for different operational units at the same level to interconnect. Furthermore, with the diversification of warfare, the three types of nodes in traditional C2 network models are insufficient to encompass all operational units. In response, this paper proposes a method for edge weighting in C2 networks based on a combination of node attributes and network attributes described by complex network theory. The node attributes mainly include node information transmission capacity, task coordination ability between nodes, node distance, and response time. The network attributes are primarily represented by hierarchy and betweenness centrality. Additionally, the traditional C2 network model's three types of nodes are expanded to five types of nodes. Based on the edge weighting method, internal command edges, inter‐network collaborative edges, and cross‐level command edges are generated within the C2 network. Simulation results demonstrate that the constructed C2 network model's characteristic parameters are superior to those of traditional C2 networks and collaborative C2 networks. This improvement enhances command and coordination abilities, aligns more closely with real‐world scenarios, and effectively improves network command and control efficiency.

Identification of mild cognitive impairment using multimodal 3D imaging data and graph convolutional networks

Abstract Objective. Mild cognitive impairment (MCI) is a precursor stage of dementia characterized by mild cognitive decline in one or more cognitive domains, without meeting the criteria for dementia. MCI is considered a prodromal form of Alzheimer's disease (AD). Early identification of MCI is crucial for both intervention and prevention of AD. To accurately identify MCI, a novel multimodal 3D imaging data integration graph convolutional network model is designed in this paper. Approach. The proposed model utilizes 3D-VGGNet to extract three-dimensional features from multimodal imaging data (such as sMRI and FDG-PET), which are then fused into feature vectors as the node features of a population graph. Non-imaging features of participants are combined with the multimodal imaging data to construct a population sparse graph. Additionally, in order to optimize the connectivity of the graph, we employed the Pairwise Attribute Estimation (PAE) method to compute the edge weights based on non-imaging data, thereby enhancing the effectiveness of the graph structure. Subsequently, a population-based graph convolutional network (GCN) integrates the structural and functional features of different modal images into the features of each participant for MCI classification. Main results. Experiments on the ADNI demonstrated accuracies of 98.57%, 96.03%, and 96.83% for the NC-EMCI, NC-LMCI, and EMCI-LMCI classification tasks, respectively. The AUC, specificity, sensitivity, and F1-score are also superior to state-of-the-art models, demonstrating the effectiveness of the proposed model. Furthermore, the proposed model is applied to the ABIDE dataset for autism diagnosis, achieving an accuracy of 91.43% and outperforming the state-of-the-art models, indicating excellent generalization capabilities of the proposed model. Significance. This study demonstrate the proposed model’s ability to integrate multimodal imaging data and its excellent ability to recognize MCI. This will help achieve early warning for AD and intelligent diagnosis of other brain neurodegenerative diseases.

Signed-network-based consensus control for nonlinear multi-agent systems: a dynamic encryption–decryption approach

Abstract This paper is concerned with the bipartite secure control issue for a class of discrete-time nonlinear multi-agent systems under a dynamic encryption–decryption approach. First, the coupling relationships between agents are portrayed through a signed graph topology containing the edges of positive and negative connection weights. Next, the information transmissions between agents and their neighbors are executed via a shared communication network. The dynamic encryption–decryption approach is implemented to transform original signals into ciphertexts. Under the assumption that the signed graph is structurally balanced, a signed-network-based bipartite secure controller is designed to achieve the desired state control for the nonlinear multi-agent system and sufficient conditions are obtained for the existence of the desired signed-network-based state controller. Furthermore, a precise definition of the minimum channel capacity is proposed to understand the factors affecting the minimum channel capacity. Finally, the effectiveness of the proposed approach is illustrated by two simulation examples.

The self-similarity of the multilayer networks

Abstract Research on the self-similarity of multilayer networks is scarce, when compared to the extensive research conducted on the dynamics of these networks. In this paper, we use entropy to determine the edge weights in each sub-network, and apply the degree-degree distance to unify the weight values of connecting edges between different sub-networks, and unify the edges with different meanings in the multilayer network numerically. At this time, the multilayer network is compressed into a single-layer network, also known as the aggregated network. Furthermore, the self-similarity of the multilayer network is represented by analyzing the self-similarity of the aggregate network. The study of self-similarity was conducted on two classical fractal networks and a real-world multilayer network. The results show that multilayer networks exhibit more pronounced self-similarity, and the intensity of self-similarity in multilayer networks can vary with the connection mode of sub-networks.

A Distributed Algorithm for Reaching Average Consensus in Unbalanced Tree Networks

In this paper, a distributed algorithm for reaching average consensus is proposed for multi-agent systems with tree communication graph, when the edge weight distribution is unbalanced. First, the problem is introduced as a key topic of core algorithms for several modern scenarios. Then, the relative solution is proposed as a finite-time algorithm, which can be included in any application as a preliminary setup routine, and it is well-suited to be integrated with other adaptive setup routines, thus making the proposed solution useful in several practical applications. A special focus is devoted to the integration of the proposed method with a recent Laplacian eigenvalue allocation algorithm, and the implementation of the overall approach in a wireless sensor network framework. Finally, a worked example is provided, showing the significance of this approach for reaching a more precise average consensus in uncertain scenarios.

A network analysis of voice hearing, emotional distress and subjective recovery before and after cognitive behavioural interventions.

There is a need to identify and to better understand key processes involved in voice hearing, which can inform the targeting and development of psychological interventions for distressing voices. The current study aimed to examine interrelations between the negative impact of voices, voice characteristics, emotional distress and recovery before and after cognitive behavioural interventions for voices (Coping Strategy Enhancement, guided self-help Cognitive Behavioural Therapy, Relating Therapy and Person-Based Cognitive Therapy). The sample consisted of 172 participants from the Sussex Voices Clinic who completed pre- and post-treatment assessments. The negative impact of voices, voice characteristics, emotional distress and recovery were used to estimate two networks, before and after cognitive behavioural interventions, using the graphical lasso method with the extended Bayesian information criterion. Centrality indices were also computed, and the two networks were compared on connectivity, structure and individual edge weights. Depression, anxiety and the negative impact of voices were identified as key central symptoms and acted as bridge symptoms in pre- and post-treatment networks. There were no significant differences in network structure (M = 0.155, p = .57), global strength (S = 0.188, p = .07) and centralities (C = -0.318, p = -.06) between the two networks. Our findings suggest that anxiety and depression are promising treatment targets, that can lead to reductions in voice-related distress, whereas the characteristics of voices and subjective recovery play little role in the network structure. Limitations include the lack of a control group and the lack of diversity within the sample.

First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States.

We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measurements, which are implemented on IBM quantum computers with a midcircuit readout option. Unlike classical hitting times, the statistical aspect of the problem depends on the way we construct the measured path, an effect that we quantify experimentally. First, we experimentally verify the theoretical prediction that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters, which has a well-known topological interpretation. Second, depending on the initial state, system parameters, and measurement protocol, the detection probability can be less than one or even zero, which is related to dark-state physics. Both return-time quantization and the appearance of the dark states are related to degeneracies in the eigenvalues of the unitary time evolution operator. We conclude that, for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. However, a finite number of measurements leads to broadening effects, which modify the topological quantization and chiral effects of the asymptotic theory with an infinite number of measurements.

Distributed Bipartite Consensus of Multi-Agent Systems via Disturbance Rejection Control Strategy

This work aims to focus on analyzing the consensus control problem in cooperative–competitive networks in the occurrence of external disturbances. The primary motive of this work is to employ the equivalent input-disturbance estimation technique to compensate for the impact of external disturbances in the considered multi-agent system. In particular, a suitable low-pass filter is implemented to enhance the accuracy of disturbance estimation performance. In addition, a specific signed, connected, and structurally balanced undirected communication graph with positive and negative edge weights is considered to express the cooperation–competition communication among neighboring agents. The cooperative–competitive multi-agent system reaches its final state with same magnitude and in opposite direction under the considered structurally balanced graph. By utilizing the properties of Lyapunov stability theory and graph theory, the adequate conditions assuring the bipartite consensus of the examined multi-agent system are established as linear matrix inequalities. An illustrative example is delivered at the end to check the efficacy of the designed control scheme.

THE REFLEXIVE EDGE STRENGTH OF THE PENTAGONAL SNAKE GRAPH AND CORONA OF THE OPEN TRIANGULAR LADDER AND NULL GRAPH

Assume that be an undirected simple graph with vertex set and edge set . The edge irregular reflexive -labeling of graph is a labeling selects positive integers from 1 to as edge labels and non negative even numbers from 0 to as vertex labels, and the weights assigned to each edge are distinct, where . On graph with labeling, the weight of edge is represented by which is defined as the sum of edge label and all vertex labels incident to that edge. Reflexive edge strength of graph is the minimum of the highest label, denoted by . In this research, reflexive edge strength for pentagonal snake graph and corona of open triangular ladder and null graph will be determined. The method of this research is literature study, the lower bound of determined by Ryan’s lemma and the upper bound by labeling. The reflexive edge strength of pentagonal snake graph with is for and for The reflexive edge strength of corona of open triangular ladder and null graph with n ≥ 3 and m ≥ 1 is and .

Modeling and Analysis of Public Transport Network in Hohhot Based on Complex Network

In the urban public transport network, the transfer of buses and subways provides convenience for residents to travel efficiently. But in actual operation, it is found that accidents, natural disasters, and other damage are inevitable. These sudden events may lead to route suspensions and service delays, ultimately resulting in network paralysis. In this paper, complex network theory is used to construct a weighted double-layer network model. Carrying capacity is considered the edge weight. The model analyzes the impact of these sudden events on network performance. It also conducts in-depth research on network structure and node importance. A collective influence (CI) algorithm is proposed as a centrality index to evaluate node importance. Based on the dynamic nature of the attacks, the network state is divided into initial network and current network. Taking Hohhot as an example, the results show that the network based on a CI algorithm node attack has the worst invulnerability. The network invulnerability based on an edge weight attack is better than that of edge betweenness. Compared with the current network, the invulnerability of the initial network is stronger. This indicates that ongoing changes and adaptations in the network may accelerate the decline in overall performance. At the same time, targeted interventions on key nodes and edges can enhance the network’s invulnerability. Planners can continuously monitor network performance to provide a basis for dynamic management and real-time adjustments. Additionally, effective information about critical routes to the public helps ensure the sustainable operation of the public transportation network.

The k-core in percolated dense graph sequences

Abstract We determine the order of the k-core in a large class of dense graph sequences. Let $G_n$ be a sequence of undirected, n-vertex graphs with edge weights $\{a^n_{i,j}\}_{i,j \in [n]}$ that converges to a graphon $W\colon[0,1]^2 \to [0,+\infty)$ in the cut metric. Keeping an edge (i,j) of $G_n$ with probability ${a^n_{i,j}}/{n}$ independently, we obtain a sequence of random graphs $G_n({1}/{n})$ . Using a branching process and the theory of dense graph limits, under mild assumptions we obtain the order of the k-core of random graphs $G_n({1}/{n})$ . Our result can also be used to obtain the threshold of appearance of a k-core of order n.

A Fast Algorithm for All-Pairs-Shortest-Paths Suitable for Neural Networks.

Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: if the edges are given by the adjacency matrix Aij, then with a suitably small value of γ, the shortest path distances are Dij=ceil(logγ[(I-γA)-1]ij).We derive several graph-theoretic bounds on the value of γ and explore its useful range with numerics on different graph types. Even when the distance function is not globally accurate across the entire graph, it still works locally to instruct pursuit of the shortest path. In this mode, it also extends to weighted graphs with positive edge weights. For a wide range of dense graphs, this distance function is computationally faster than the best available alternative. Finally, we show that this method leads naturally to a neural network solution of the all-pairs-shortest-path problem.

Who has the greatest influence on adolescent gaming disorder: parents, teachers, or peers? An interpersonal relationships network model of gaming disorder.

Gaming disorder (GD) in adolescents is associated with impaired interpersonal relationships, including those with parents, teachers and peers. However, the interpersonal relationships most strongly associated with GD-related maladaptive behaviors are not well established. This study aimed to investigate the associations between these three types of relationships and the manifestation of GD in adolescents. In this cross-sectional study, 1920 Chinese adolescents participated in a survey that assessed interpersonal relationships (parent-child, teacher-student, and peer relationships) and demographic variables (e.g., gender, grade, duration of gaming), and 1414 participants were ultimately included. A network analysis approach was utilized to evaluate the key network metrics of edge weight and node centrality. The findings revealed that peer fear and inferiority (r = 0.12) and teacher-student conflict were most strongly correlated with GD, followed by parent-child conflict (r = 0.09). Peer fear and inferiority exhibited the highest strength centrality (0.84), followed by teacher-student conflict (0.83) and parent-child conflict (0.35). Moreover, the duration of gaming was significantly and positively correlated with GD (r = 0.19). The present study underscores the significant role of conflict and rejection within interpersonal relationships, particularly among peers, in the manifestation of GD-related behaviors in Chinese adolescents.

The rank of sparse symmetric matrices over arbitrary fields

AbstractLet be an arbitrary field and be a sequence of sparse weighted Erdős–Rényi random graphs on vertices with edge probability , where weights from are assigned to the edges according to a matrix . We show that the normalized rank of the adjacency matrix of converges to a constant, and derive the limiting expression. Our result shows that for the general class of sparse symmetric matrices under consideration, the asymptotics of the normalized rank are independent of the edge weights and even the field, in the sense that the limiting constant for the general case coincides with the one previously established for adjacency matrices of sparse nonweighted Erdős–Rényi matrices over . Our proof, which is purely combinatorial in its nature, is based on an intricate extension of a novel perturbation approach to the symmetric setting.

An Algorithm for Predicting Vehicle Behavior in High-Speed Scenes Using Visual and Dynamic Graphical Neural Network Inference

Accidents caused by vehicles changing lanes occur frequently on highways. Moreover, frequent lane changes can severely impact traffic flow during peak commuting hours and on busy roads. A novel framework based on a multi-relational graph convolutional network (MR-GCN) is herein proposed to address these challenges. First, a dynamic multilevel relational graph was designed to describe interactions between vehicles and road objects at different spatio-temporal granularities, with real-time updates to edge weights to enhance understanding of complex traffic scenarios. Second, an improved spatio-temporal interaction graph generation method was introduced, focusing on spatio-temporal variations and capturing complex interaction patterns to enhance prediction accuracy and adaptability. Finally, by integrating a dynamic multi-relational graph convolutional network (DMR-GCN) with dynamic scene sensing and interaction learning mechanisms, the framework enables real-time updates of complex vehicle relationships, thereby improving behavior prediction’s accuracy and real-time performance. Experimental validation on multiple benchmark datasets, including KITTI, Apollo, and Indian, showed that our algorithmic framework achieves significant performance improvements in vehicle behavior prediction tasks, with Map, Recall, and F1 scores reaching 90%, 88%, and 89%, respectively, outperforming existing algorithms. Additionally, the model achieved a Map of 91%, a Recall of 89%, and an F1 score of 90% under congested road conditions in a self-collected high-speed traffic scenario dataset, further demonstrating its robustness and adaptability in high-speed traffic conditions. These results show that the proposed model is highly practical and stable in real-world applications such as traffic control systems and self-driving vehicles, providing strong support for efficient vehicle behavior prediction.

Component-based modeling of cascading failure propagation in directed dual-weight software networks

Software vulnerabilities often lead to cascading failures, resulting in service unavailability and potential breaches of user data. However, existing models for cascading failure propagation typically focus solely on the static design’s calling relationships, disregarding dynamic runtime propagation paths. Moreover, current network topology models primarily consider function calling frequency while overlooking critical factors like internal failure probability and component failure tolerance rates. Yet, these factors significantly influence the actual propagation of software cascading failures. In this study, we address these limitations by incorporating internal failure probabilities and calling frequencies as node and edge weights, respectively. This forms the basis of our component-based directed dual-weight software network cascading failure propagation model. This model encompasses the evaluation of cascading failure propagation through intra-component and inter-component propagation probabilities, alongside the constraint of component failure tolerance rates. Through extensive experiments conducted on six real-world software applications, our model has demonstrated its effectiveness in predicting software cascading failure propagation processes. This method deepens our understanding of software failures and structures, equipping software testers with the knowledge to make well-informed judgments regarding software quality concerns.

SpaGRA: Graph augmentation facilitates domain identification for spatially resolved transcriptomics

Recent advances in spatially resolved transcriptomics (SRT) have provided new opportunities for characterizing spatial structures of various tissues. Graph-based geometric deep learning have gained widespread adoption for spatial domain identification tasks. Currently, most methods define adjacency relation between cells or spots by their spatial distance in SRT data, which overlooks key biological interactions like gene expression similarities, and leads to inaccuracies in spatial domain identification. To tackle this challenge, we propose a novel method, SpaGRA (https://github.com/sunxue-yy/SpaGRA), for automatic multi-relationship construction based on graph augmentation. SpaGRA uses spatial distance as prior knowledge and dynamically adjusts edge weights with multi-head graph attention networks (GATs). This helps SpaGRA to uncover diverse node relationships and enhance message passing in geometric contrastive learning. Additionally, SpaGRA uses these multi-view relationships to construct negative samples, addressing sampling bias posed by random selection. Experimental results show that SpaGRA demonstrates superior domain identification performance on multiple datasets generated from different protocols. Using SpaGRA, we analyzed the functional regions in the mouse hypothalamus, identified key genes related to heart development in mouse embryos, and observed cancer-associated fibroblasts enveloping cancer cells in the latest Visium HD data. Overall, SpaGRA can effectively characterize spatial structures across diverse SRT datasets.