Graph Topology Research Articles

Deep graph layer information mining convolutional network

Graph convolution network is a powerful method of deep learning of graph structure data. Existing methods usually adjust the neighborhood information aggregation mode or optimize the graph topology layer by layer for improving the graph convolution network. However, these methods seldom consider the discriminative information about hierarchical characteristics nodes (some special nodes only can be correctly classified in one layer and are the misclassification nodes in the other layers of deep graph convolutional networks) in the different layers for complementing the neighborhood topology information. To further find these information, a deep graph layer information mining convolutional network (GLIM) can alternately measure the neighborhood ranking information on topology structure and update the residual identity mapping node information on the different layers for enhancing the model classification performance. Moreover, GLIM can construct a unified framework with the various hyper-parameters for the different graph learning method based on graph convolution network. Experiments show GLIM outperforms the state-of-the-art methods for semi-supervised node classification in three cite datasets (Cora, CiteSeer,and PubMed) and three image datasets (MNIST, Cifar10 and Cifar100).

Computation of molecular description of supramolecular Fuchsine model useful in medical data

Supramolecular chemistry is a fascinating field that explores the interactions between molecules to create higher-order structures. In the case of the supramolecular chain of Fuchsine acid, which is a type of dye molecule, several chemical applications are possible. Fuchsine acid helps to make better medicine carriers that deliver drugs where they’re needed in the body, making treatments more effective and reducing side effects. It also helps create smart materials like sensors and self-fixing plastics, which are useful in electronics, keeping our environment clean, and making new materials. In sensing and detection, the supramolecular chain of Fuchsine acid utilizes as a sensor or detector for specific analyzes. In drug delivery, the supramolecular chains of Fuchsine acid incorporated into drug delivery systems. In recent years, a common method is linking a graph to a chemical structure and using topological descriptors to study it. This technique is becoming increasingly important over time. Topological descriptors gives very useful information while studying the topology of chemical graph. In this paper, we have computed the 3D structure of supramolecular graph of Fuchsine acid. We have computed an explicit expressions of ABC index, GA index, General Randic´\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\acute{c}$$\\end{document} index, first and second Zagreb index, hyper Zagreb index, H-index and F-index of supramolecular structure of Fushine acid.

On the sensitivity of centrality metrics

Despite the huge importance that the centrality metrics have in understanding the topology of a network, too little is known about the effects that small alterations in the topology of the input graph induce in the norm of the vector that stores the node centralities. If so, then it could be possible to avoid re-calculating the vector of centrality metrics if some minimal changes occur in the network topology, which would allow for significant computational savings. Hence, after formalising the notion of centrality, three of the most basic metrics were herein considered (i.e., Degree, Eigenvector, and Katz centrality). To perform the simulations, two probabilistic failure models were used to describe alterations in network topology: Uniform (i.e., all nodes can be independently deleted from the network with a fixed probability) and Best Connected (i.e., the probability a node is removed depends on its degree). Our analysis suggests that, in the case of degree, small variations in the topology of the input graph determine small variations in Degree centrality, independently of the topological features of the input graph; conversely, both Eigenvector and Katz centralities can be extremely sensitive to changes in the topology of the input graph. In other words, if the input graph has some specific features, even small changes in the topology of the input graph can have catastrophic effects on the Eigenvector or Katz centrality.

On topological conditions for enabling transient control in leader–follower networks

We derive necessary and sufficient conditions for leader–follower multi-agent systems such that we can further apply prescribed performance control to achieve the desired formation while satisfying certain transient constraints. A leader–follower framework is considered in the sense that a group of agents with external inputs are selected as leaders in order to drive the group of followers in a way that the entire system can achieve target formation within certain prescribed performance transient bounds. We first derive necessary conditions on the leader–follower graph topology under which the target formation together with the prescribed performance guarantees can be fulfilled. Afterwards, the derived necessary conditions are extended to necessary and sufficient conditions for leader–follower formation control under transient constraints. Finally, the proposed results are illustrated with simulation examples.

Patterns of Service Utilization across the Full Continuum of Care: Using Patient Journeys to Assess Disparities in Access to Health Services

Healthcare organizations have a contractual obligation to the public to address population-level inequities to health services access and shed light on them. Various studies have focused on achieving equitable access to healthcare services for vulnerable patients. However, these studies do not provide a nuanced perspective based on the local reality across the full continuum of care. In previous work, graph topology was used to provide visual depictions of the dynamics of patients’ movement across a complex healthcare system. Using patients’ encounters data represented as a graph, this study expands on previous work and proposes a methodology to identify and quantify cohort-specific disparities in accessing healthcare services across the continuum of care. The result has demonstrated that a more nuanced approach to assessing access-to-care disparity is doable using patients’ patterns of service utilization from a longitudinal cross-continuum healthcare dataset. The proposed method can be used as part of a toolkit to support healthcare organizations that wish to structure their services to provide better care to their vulnerable populations based on the local realities. This provides a first step in addressing inequities for vulnerable patients in accessing healthcare services. However, additional steps need to be considered to fully address these inequities.

Graph-based minimum error entropy Kalman filtering

When the Gaussian kernel function is chosen with a small kernel bandwidths, the minimum error entropy Kalman filter (MEEKF) exhibits excellent performance. However, further narrowing the kernel bandwidths leads to a degradation in performance. To address this issue, this paper proposed a Graph-based MEEKF (G-MEEKF) algorithm based on Graph Signal Processing (GSP) theory. The G-MEEKF algorithm addresses the problem by smoothing the errors using graph filtering and incorporating graph topology into the cost function. The convergence of the algorithm is theoretically analyzed and simulations demonstrate that G-MEEKF improves the performance of MEEKF under small kernel bandwidths. Furthermore, it is emphasized that the topology of the graph abstracted from the minimum error entropy (MEE) definition also influences the performance of the algorithm.

Low-complexity collaborative caching strategy based on spatio-temporal graph convolutional model

To meet the low delay requirements for data content access in industrial IoT, efficient content caching strategies need to be designed in the Mobile Edge Computing (MEC). Most existing caching policies reduce access delay by predicting content popularity and caching popular content earlier during off-peak traffic, but these strategies only focus on the temporal order of content popularity without fully considering the graph topology of MEC servers and ignore the spatial correlation of content popularity. This paper proposes a low-complexity collaborative caching strategy based on spatio-temporal graph convolutional model (STCC). We integrate graph convolutional neural network and gated recurrent unit to construct spatio-temporal graph convolutional model, which mines the spatio-temporal correlation features of content popularity and make effective predictions on the MEC server graph topology constructed by proximity and semantic relations. Furthermore, we use hierarchical clustering to classify MEC servers into collaborative domains and design a low-complexity heuristic collaborative caching content placement algorithm to minimize the average access delay. Compared with the existing MEC server caching strategy, simulation experiments show that STCC has a better prediction effect of content popularity, and achieves better performance in the two indicators of the cache hit ratio and average access delay.

DSTN: Dynamic Spatio-Temporal Network for Early Fault Warning in Chemical Processes

Multivariate time series prediction, especially in early fault warning for chemical processes, poses significant challenges. The advent of graph neural network (GNN) method has made breakthroughs in this domain by enabling the processing of topological data. However, the traditional methods suffer from the issue of over-smoothing and inability to capture intricate multi-scale spatio-temporal dependencies. Additionally, the existing graph structures fall short in describing the complex spatial relationships among multi-stage sensors, impeding their adaptability to dynamically evolving chain reaction scenarios. To alleviate these limitations, a novel Dynamic spatio-Temporal Network for early fault warning in chemical processes, named DSTN for short, is proposed in this paper. We extract the spatial and temporal features of the time series by the designed dynamic GNN and the improved Transformer network. Then, we integrate the spatio-temporal features through the residual network. DSTN has the following advantages: (1) A one-dimensional convolutional neural network is seamlessly incorporated into the Transformer architecture for bolstering its capacity to discern both global and local features within time series. (2) The continuous sliding window and mutual information methods are employed to construct a dynamic topology graph, and a K-order adjacency matrix is designed to rectify the inefficiencies in learning weights associated with convolution kernel parameters. (3) Multiple spatio-temporal modules interconnected via residual connection to adaptively fuse multi-scale features. Experimental results demonstrate that our proposed DSTN method outperforms existing methods in terms of both performance and interpretability in early fault warning of chemical processes.

Sampling theory of jointly bandlimited time-vertex graph signals

Time-vertex graph signal (TVGS) models describe time-varying data with irregular structures. The bandlimitedness in the joint time-vertex Fourier spectral domain reflects smoothness in both temporal and graph topology. In this paper, we study the critical sampling of three types of TVGS including continuous-time signals, infinite-length sequences, and finite-length sequences in the time domain for each vertex on the graph. For a jointly bandlimited TVGS, we prove a lower bound on sampling density or sampling ratio, which depends on the measure of the spectral support in the joint time-vertex Fourier spectral domain. We also provide a lower bound on the sampling density or sampling ratio of each vertex on sampling sets for perfect recovery. To demonstrate that critical sampling is achievable, we propose the sampling and reconstruction procedures for the different types of TVGS. Finally, we show how the proposed sampling schemes can be applied to numerical as well as real datasets.

DBGCN

Given the extensive use of online learning in educational settings, Knowledge Tracing (KT) is becoming increasingly essential. KT primarily aims to predict a student's future knowledge acquisition based on their past learning activities, thus enhancing the efficiency of student learning. However, the effective acquisition of dynamic and evolving student representations from their historical records presents a formidable challenge. This paper introduces a Knowledge Tracing methodology predicated on Dynamic Broadth Graph Convolutional Networks (DBGCN). DBGCN leverages the mechanisms of breadth graph convolutional networks to proficiently acquire representations of questions and knowledge points from dynamically constructed topological graphs. It employs student state information as an attention query vector to augment student representations, thereby partially mitigating the challenge of capturing the dynamic shifts in user states. The effectiveness of our proposed DBGCN method has been demonstrated through extensive experimentation.

The maximum genus of the generalized Petersen Graph, GP (<em>n, k</em>) for the cases <em>k</em> = 1, 2

In Topological graph theory, the maximum genus of graphs has been a fascinating subject. For a simple connected graph G, the maximum genus γM(G) is the largest genus of an orientable surface on which G has a 2-cell embedding. γM(G) has the upper bound, γM(G)≤[β/2], where β(G) denotes the Betti number and G is said to be upper embeddable if the equality holds. In this study, the maximum genus of GP(n, k) is established as γM(GP(n,k))=[(n+1)/2] for k = 1 and k = 2 by proving the upper embeddability of generalized Petersen graph, GP(n, k) for the cases k = 1 and k = 2. The proof is done by obtaining spanning trees T and examining the components in the edge complements GP(n, k)\T for the cases k = 1 and k = 2 of GP(n, k).

AAGCN: a graph convolutional neural network with adaptive feature and topology learning

In recent years, there has been a growing prevalence of deep learning in various domains, owing to advancements in information technology and computing power. Graph neural network methods within deep learning have shown remarkable capabilities in processing graph-structured data, such as social networks and traffic networks. As a result, they have garnered significant attention from researchers.However, real-world data often face challenges like data sparsity and missing labels, which can hinder the performance and generalization ability of graph convolutional neural networks. To overcome these challenges, our research aims to effectively extract the hidden features and topological information of graph convolutional neural networks. We propose an innovative model called Adaptive Feature and Topology Graph Convolutional Neural Network (AAGCN). By incorporating an adaptive layer, our model preprocesses the data and integrates the hidden features and topological information with the original data’s features and structure. These fused features are then utilized in the convolutional layer for training, significantly enhancing the expressive power of graph convolutional neural networks.To evaluate the effectiveness of the adaptive layer in the AAGCN model, we conducted node classification experiments on real datasets. The results validate its ability to address data sparsity and improve the classification performance of graph convolutional neural networks.In conclusion, our research primarily focuses on addressing data sparsity and missing labels in graph convolutional neural networks. The proposed AAGCN model, which incorporates an adaptive layer, effectively extracts hidden features and topological information, thereby enhancing the expressive power and classification performance of these networks.

Efficient Unsupervised Community Search with Pre-Trained Graph Transformer

Community search has aroused widespread interest in the past decades. Among existing solutions, the learning-based models exhibit outstanding performance in terms of accuracy by leveraging labels to 1) train the model for community score learning, and 2) select the optimal threshold for community identification. However, labeled data are not always available in real-world scenarios. To address this notable limitation of learning-based models, we propose a pre-trained graph Trans former based community search framework that uses Zero label (i.e., unsupervised), termed TransZero. TransZero has two key phases, i.e., the offline pre-training phase and the online search phase. Specifically, in the offline pre-training phase, we design an efficient and effective community search graph transformer ( CSGphormer ) to learn node representation. To pre-train CSGphormer without the usage of labels, we introduce two self-supervised losses, i.e., personalization loss and link loss, motivated by the inherent uniqueness of node and graph topology, respectively. In the online search phase, with the representation learned by the pre-trained CSGphormer , we compute the community score without using labels by measuring the similarity of representations between the query nodes and the nodes in the graph. To free the framework from the usage of a label-based threshold, we define a new function named expected score gain to guide the community identification process. Furthermore, we propose two efficient and effective algorithms for the community identification process that run without the usage of labels. Extensive experiments over 10 public datasets illustrate the superior performance of TransZero regarding both accuracy and efficiency.

Ship Ballast Water System Fault Diagnosis Method Based on Multi-Feature Fusion Graph Convolution

To tackle the issues of limited fault data, inadequate information availability, and subpar fault diagnosis within the realm of ship ballast water system condition monitoring, this paper presents a novel fault diagnosis methodology known as the Probabilistic Similarity and Linear Similarity-based Graph Convolutional Neural Network (PCGCN) model. PCGCN initially converts the ship’s ballast water system dataset into two distinct graph structures: a probabilistic topology graph and a correlation topology graph. It delves into data similarity by employing T-SNE for probabilistic similarity and Pearson’s correlation coefficient for linear similarity to establish the inter-sample neighbor relationships. Subsequently, an early fusion of these two graph structures is conducted to extract more profound multi-scale feature information. Following this step, the graph convolutional neural network (GCN) is introduced to amalgamate the feature information from neighboring nodes in addition to its inherent features. This is aimed at enhancing the available information for the classification task and addressing the issues of limited fault data and inadequate label information. In conclusion, we employ a simulated ship fault dataset for testing experiments, and the PCGCN model demonstrates superior classification accuracy, reaching 97.49%, outperforming traditional diagnostic methods. These experimental outcomes underscore the applicability of the model introduced in this study to the realm of ship ballast water system fault diagnosis, even under challenging conditions characterized by limited sample sizes and insufficient labeling information.

Fast Graph Generation via Spectral Diffusion.

Generating graph-structured data is a challenging problem, which requires learning the underlying distribution of graphs. Various models such as graph VAE, graph GANs, and graph diffusion models have been proposed to generate meaningful and reliable graphs, among which the diffusion models have achieved state-of-the-art performance. In this paper, we argue that running full-rank diffusion SDEs on the whole graph adjacency matrix space hinders diffusion models from learning graph topology generation, and hence significantly deteriorates the quality of generated graph data. To address this limitation, we propose an efficient yet effective Graph Spectral Diffusion Model (GSDM), which is driven by low-rank diffusion SDEs on the graph spectrum space. Our spectral diffusion model is further proven to enjoy a substantially stronger theoretical guarantee than standard diffusion models. Extensive experiments across various datasets demonstrate that our proposed GSDM turns out to be the SOTA model, by exhibiting both significantly higher generation quality and much less computational consumption than the baselines.

Algorithmic approach to discrete fracture network flow modeling in consideration of realistic connections in large-scale fracture networks

Analyzing rock mass seepage using the discrete fracture network (DFN) flow model poses challenges when dealing with complex fracture networks. This paper presents a novel DFN flow model that incorporates the actual connections of large-scale fractures. Notably, this model efficiently manages over 20,000 fractures without necessitating adjustments to the DFN geometry. All geometric analyses, such as identifying connected fractures, dividing the two-dimensional domain into closed loops, triangulating arbitrary loops, and refining triangular elements, are fully automated. The analysis processes are comprehensively introduced, and core algorithms, along with their pseudo-codes, are outlined and explained to assist readers in their programming endeavors. The accuracy of geometric analyses is validated through topological graphs representing the connection relationships between fractures. In practical application, the proposed model is employed to assess the water-sealing effectiveness of an underground storage cavern project. The analysis results indicate that the existing design scheme can effectively prevent the stored oil from leaking in the presence of both dense and sparse fractures. Furthermore, following extensive modification and optimization, the scale and precision of model computation suggest that the proposed model and developed codes can meet the requirements of engineering applications.

Optimizing energy storage plant discrete system dynamics analysis with graph convolutional networks

Addressing the challenges of suboptimal model performance and excessive parameters and operations in the optimization of energy storage power plants utilizing Graph Convolutional Network (GCN), this paper introduces a novel approach – the packet-switched graph convolutional network. Initially, a GCN extreme learning machine is established. Drawing inspiration from this solid foundation, we have innovatively crafted a group exchange graph convolution module. This module leverages group graph convolution techniques to amalgamate unique node feature information, tailored to diverse topology graph matrices based on various groupings. This innovative approach ensures that information flows freely and effectively among distinct groupings. Furthermore, we have designed a cutting-edge timing depth separation convolution module, comprising two innovative components. The first component introduces timing depth separation convolution, revolutionizing the original timing convolution module. The second component, the packet-switching graph convolutional network, revolutionizes the time sequence depth separation convolution process. It achieves this by employing 1 × 1 convolutional layers between different feature fusion packets, enabling seamless information exchange between distinct packets. Experimental results demonstrate the efficacy of the proposed model, with root mean square error (RMSE) metrics and root mean square error (MAE) metrics for single-step prediction reaching 46.08 and 26.22 at 60 min, respectively. In multi-step testing, the proposed model exhibits a 14.71 % reduction in RMSE error at the 15-min scale and a 9.29 % reduction at the 60-min scale compared to the benchmark model. This performance improvement enhances the operational efficiency and reliability of the energy storage plant, particularly under dynamic changes in the time series.

A brain topography graph embedded convolutional neural network for EEG-based motor imagery classification

Brain-computer interface (BCI) based on motor imagery EEG (MI-EEG) has been used extensively in health care, device control, entertainment, and other fields. MI-EEG signals consist of multiple channels that exhibit a specific topological relationship. However, many existing methods based on deep learning do not make good use of the multi-electrode characteristics of EEG signals. To further improve the decoding performance of MI-EEG, this study proposes a novel method combining the brain topology graph embedding and convolutional neural network (CNN) for MI-EEG classification. Specifically, mutual information is used to measure the relationship between EEG channels. A graph convolutional network (GCN) is employed to embed the topological relationship. Following this, a convolutional block using depth-wise convolution is built to extract spatial–temporal features, while a temporal convolutional network (TCN) is used to extract advanced temporal features. The model’s performance is evaluated on BCICIV-2a and HGD datasets. The experimental results show that the classification accuracy of the proposed model is 80.46% and 94.38%, respectively, outperforming existing methods. Moreover, ablation experiments and feature visualization show that graph embedding can significantly improve the decoding performance of MI-EEG.

The Block Topological Space and Block Topological Graph Induced by Undirected Graphs

Let $G=(V(G),E(G))$ be a simple undirected graph. A \textit{block} of $G$ is a maximal connected subgraph of $G$ that contains no cut-vertices \cite{eric}. The family of vertex sets of blocks of $G$ generates a unique topology. In this paper, we formally define the topology generated by the family of blocks in a graph called the \textit{block topological space}. Moreover, we characterize and describe some special attributes of the block topological space. Finally, we associate a corresponding graph from a given block topological space by defining the \textit{block topological graph}.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM<R0. For RM,R0>1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.