Edges Of Graph Research Articles

TGCN-Bert Emoji Prediction in Information Systems Using TCN and GCN Fusing Features Based on BERT

In recent studies, graph convolutional neural networks (GCNs) have been used to solve different natural language processing (NLP) tasks. However, few researches apply graph convolutional networks to short text classification. Emoji prediction, as a complex sentiment analysis task, has received even less attention. In this work, the authors propose TGCN-Bert which combines pre-trained BERT temporal convolutional networks (TCNs) and graph convolutional networks for short text classification and emoji prediction. They initialize the nodes with the help of BERT and define the edges in text graph based on the term frequency-inverse document frequency (TF-IDF) and positive point-wise mutual information (PPMI). They employ the model for emoji prediction task, and a metric based on emoji clustering is developed to better measure the validity of emoji prediction results. To validate the performance of TGCN-Bert, they compare it with other GCN variants on short text classification datasets and emoji prediction datasets; experiments show that TGCN-Bert achieves better performance.

MuCoGraph: A multi-scale constraint enhanced pose-graph framework for MLS point cloud inconsistency correction

The position consistency of mobile laser scanning (MLS) point clouds is crucial for large-scale applications, and is normally guaranteed by the global navigation satellite system (GNSS) and high-precision inertial measurement unit (IMU) in the data acquisition. However, GNSS-denied environments such as city valleys result in significant position inconsistency for overlapping areas, and it is difficult to automatically locate these inconsistent areas. In this paper, to overcome these problems, we present MuCoGraph, which introduces multi-scale constraints to establish the correct correspondences for revisited areas, and formulates an enhanced pose graph for position inconsistency correction. The georeferenced MLS point cloud is first sliced into segments adaptively, and these segments are then abstracted as graph vertices, which satisfy local geometric consistency and rigid transformation hypotheses. Accurate revisited graph edges are then constructed hierarchically under multi-scale scenery consistency constraints. These revisited edges are initialized based on feature-based correspondence estimation and further unreliable edge pruning. Finally, through combination with virtual co-observations, correspondence-enhanced pose-graph optimization is introduced to globally redistribute the errors and obtain a high-precision point cloud. The proposed method was used to correct the MLS point cloud position inconsistency in three datasets. The average three-dimensional distance of the checkpoints was reduced from 0.362 m, 0.108 m, and 1.027 m to 0.057 m, 0.033 m, and 0.051 m for datasets I, II, and III respectively. In addition, the root-mean-square error of all three datasets was less than 0.04 m after correction. The experiments confirmed that the proposed method can automatically locate and correct the position inconsistency of MLS point clouds, showing good robustness and effectiveness.

Bounds on the parameters of non- L -borderenergetic graphs

UDC 519.17 We consider graphs such that their Laplacian energy is equivalent to the Laplacian energy of the complete graph of the same order, which is called an L -borderenergetic graph. Firstly, we study the graphs with degree sequence consisting of at most three distinct integers and give new bounds for the number of vertices of these graphs to be non- L -borderenergetic. Second, by using Koolen–Moulton and McClelland inequalities, we give new bounds for the number of edges of a non- L -borderenergetic graph. Third, we use recent bounds given by Milovanovic, et al. on Laplacian energy to get similar conditions for non- L -borderenergetic graphs. Our bounds depend only on the degree sequence of a graph, which is much easier than computing the spectrum of the graph. In other words, we developed a faster approach to exclude non- L -borderenergetic graphs.

Gaps between consecutive eigenvalues for compact metric graphs

On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap λ2−λ1 is established, with a constant that depends only on the total length of the graph and minimum edge length. We also prove some improvements of known upper bounds for eigenvalue gaps and ratios for metric trees and extensions to certain other types of graphs.

A Comparative Study of Fuzzy Domination and Fuzzy Coloring in an Optimal Approach

An optimal network refers to a computer or communication network designed, configured, and managed to maximize efficiency, performance, and effectiveness while minimizing cost and resource utilization. In a network design and management context, optimal typically implies achieving the best possible outcomes between various factors. This research investigated the use of fuzzy graph edge coloring for various fuzzy graph operations, and it focused on the efficacy and efficiency of the fuzzy network product using the minimal spanning tree and the chromatic index of the fuzzy network product. As a network made of nodes and vertices, measurement with vertices is a parameter for domination, and edge measurement is a parameter for edge coloring, so we used these two parameters in the algorithm. This paper aims to identify an optimal network that can be established using product outcomes. This study shows a way to find an optimal fuzzy network based on comparative optimal parameter domination and edge coloring, which can be elaborated with applications. An algorithm was generated using an optimal approach, which was subsequently implemented in the form of applications.

The longest edge of the one-dimensional soft random geometric graph with boundaries

The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of such models related to connectivity structures have been studied extensively. In this article, we study the random graph from the perspective of extreme value theory and focus on the occurrence of single long edges. The model we investigate has non-periodic boundary and is parameterized by a positive constant α, which is the power for the polynomial decay of the probabilities determining the presence of an edge. As a main result, we provide a precise description of the magnitude of the longest edge in terms of asymptotic behavior in distribution. Thereby we illustrate a crucial dependence on the power α and we recover a phase transition which coincides with exactly the same phases in Benjamini and Berger[ 2 ].

Extremal graphs without long paths and large cliques

Let F be a family of graphs. A graph is called F-free if it does not contain any member of F as a subgraph. The Turán number of F is the maximum number of edges in an n-vertex F-free graph and is denoted by ex(n,F). The same maximum under the additional condition that the graphs are connected is exconn(n,F). Let Pk be the path on k vertices, Km be the clique on m vertices. We determine ex(n,{Pk,Km}) if k>2m−1 and exconn(n,{Pk,Km}) if k>m for sufficiently large n.

Depth-defying OOF-GNN: Sailing smoothly amidst GNN waves

When it comes to machine learning on graphs, Graph Neural Networks(GNNs) is a potent tool. By iteratively propagating neural messages along the edges of the input graph, GNNs integrate node feature information with graph structure. Nonetheless, not all neighborhood data is valuable. Some of the neighbor data may not be necessary for the downstream task. For a controlled and relevant information aggregation, we propose a flexible method OOF-GNN (Over-smoothing and Over-squashing Free Graph Neural Network). The main notion of this technique is to limit the impact of irrelevant and excessive information propagation during message passing. An extensive discussion of the theoretical and experimental justifications, associated with this method is presented. This technique works on all baseline models (e.g. GCN, GraphSAGE, and GAT). It allows them to gather information from the K-hop neighborhood without node information being over-smoothed and over-squashed. The efficacy of OFF-GNN in addressing the challenges of under-reaching, over-smoothing, and over-squashing, as well as improving the performance of GNN models in node classification tasks, has been demonstrated through comprehensive experimentation on both academic benchmarks and real-world datasets.

Covering the Edges of a Complete Geometric Graph with Convex Polygons

Covering the Edges of a Complete Geometric Graph with Convex Polygons

FPGN: follower prediction framework for infectious disease prevention

In recent years, how to prevent the widespread transmission of infectious diseases in communities has been a research hot spot. Tracing close contact with infected individuals is one of the most severe problems. In this work, we present a model called Follower Prediction Graph Network (FPGN) to identify high-risk visitors, which is known as follower prediction. The model is designed to identify visitors who may be infected with a disease by tracking their activities at the exact location of infected visitors. FPGN is inspired by the state-of-the-art temporal graph edge prediction algorithm TGN and draws on the shortcomings of existing algorithms. It utilizes graph structure information based on (alpha , beta )-core, time interval statistics by using the statistics of timestamp information, and a GAT-based prediction module to achieve high accuracy in follower prediction. Extensive experiments are conducted on two real datasets, demonstrating the progress of FPGN. The experimental results show that FPGN can achieve the highest results compared with other SOTA baselines. Its AP scores are higher than 0.46, and its AUC scores are higher than 0.62.

Traffic Agents Trajectory Prediction Based on Spatial-Temporal Interaction Attention.

Trajectory prediction aims to predict the movement intention of traffic participants in the future based on the historical observation trajectories. For traffic scenarios, pedestrians, vehicles and other traffic participants have social interaction of surrounding traffic participants in both time and spatial dimensions. Most previous studies only use pooling methods to simulate the interaction process between participants and cannot fully capture the spatio-temporal dependence, possibly accumulating errors with the increase in prediction time. To overcome these problems, we propose the Spatial-Temporal Interaction Attention-based Trajectory Prediction Network (STIA-TPNet), which can effectively model the spatial-temporal interaction information. Based on trajectory feature extraction, the novel Spatial-Temporal Interaction Attention Module (STIA Module) is proposed to extract the interaction relationships between traffic participants, including temporal interaction attention, spatial interaction attention, and spatio-temporal attention fusion. By adaptive allocation of attention weights, temporal interaction attention is a temporal attention mechanism used to capture the movement pattern of each traffic participant in the scene, which can learn the importance of historical trajectories at different moments to future behaviors. Since the participants number in recent traffic scenes dynamically changes, the spatial interaction attention is designed to abstract the traffic participants in the scene into graph nodes, and abstract the social interaction between participants into graph edges. Coupling the temporal and spatial interaction attentions can adaptively model the temporal-spatial information and achieve accurate trajectory prediction. By performing experiments on the INTERACTION dataset and the UTP (Unmanned Aerial Vehicle-based Trajectory Prediction) dataset, the experimental results show that the proposed method significantly improves the accuracy of trajectory prediction and outperforms the representative methods in comparison.

Hybrid path planning based on adaptive visibility graph initialization and edge computing for mobile robots

This paper presents a new initialization method that combines adaptive visibility graphs and the A* algorithm to improve the exploration, accuracy, and computing efficiency of hybrid path planning for mobile robots. First, segments/links in the full visibility graphs are removed randomly in an iterative and adaptive manner, yielding adaptive visibility graphs. Then the A* algorithm is applied to find the shortest paths in these adaptive visibility graphs. Next, high-quality paths featuring low fitness values are chosen to initialize the subsequent heuristic optimization in hybrid path planning. Specifically, in the present study, the genetic algorithm (GA) is implemented on a CPU/GPU edge computing device (Jetson AGX Xavier) to exploit its massively parallel processing threads, and the strategy for judicious CPU/GPU resource utilization is also developed. Numerical experiments are conducted to determine proper hyperparameters and configure GA with balanced performance. Various optimal paths with differential consideration of practical factors for robot path planning are obtained by the proposed method. Compared to the other benchmark methods, ours significantly improves the diversity of initial path and exploration, optimization accuracy, and computing speed (within 5 s with most less than 2 s). Furthermore, real-time experiments are carried out to demonstrate the effectiveness and application of the proposed algorithm on mobile robots.

Constructing extremal triangle-free graphs using integer programming

The maximum number of edges in a graph with matching number m and maximum degree d has been determined in Chvátal and Hanson (1976) and Balachandran and Khare (2009), where some extremal graphs have also been provided. Then, a new question has emerged: how the maximum edge count is affected by forbidding some subgraphs occurring in these extremal graphs? In Ahanjideh et al. (2022), the problem is solved in triangle-free graphs for d≥m, and for d<m with either Z(d)≤m<2d or d≤6, where Z(d) is approximately 5d/4. The authors derived structural properties of triangle-free extremal graphs, which allows us to focus on constructing small extremal components to form an extremal graph. Based on these findings, in this paper, we develop an integer programming formulation for constructing extremal graphs. Since our formulation is highly symmetric, we use our own implementation of Orbital Branching to reduce symmetry. We also implement our integer programming formulation so that the feasible region is restricted iteratively. Using a combination of the two approaches, we expand the solution into d≤10 instead of d≤6 for m>d. Our results endorse the formula for the number of edges in all extremal triangle-free graphs conjectured in Ahanjideh et al. (2022).

On graphs that contain exactly k copies of a subgraph, and a related problem in search theory

We study exak(n,F), the largest number of edges in an n-vertex graph that contains exactly k copies of a given subgraph F. The case k=0 is the Turán number ex(n,F) that is among the most studied parameters in extremal graph theory. We show that for any F and k, exak(n,F)=(1+o(1))ex(n,F) and determine the exact values of exak(n,K3) and exa1(n,Kr) for n large enough. We also explore a connection to the following well-known problem in search theory. We are given a graph of order n that consists of an unknown copy of F and some isolated vertices. We can ask pairs of vertices as queries, and the answer tells us whether there is an edge between those vertices. Our goal is to describe the graph using as few queries as possible. Aigner and Triesch in 1990 showed that the number of queries needed is at least n2−exa1(n,F). Among other results we show that the number of queries that were answered NO is at least n2−exa1(n,F).

MuxGNN: Multiplex Graph Neural Network for Heterogeneous Graphs.

Graph neural networks (GNNs) have become effective learning techniques for many downstream network mining tasks including node and graph classification, link prediction, and network reconstruction. However, most GNN methods have been developed for homogeneous networks with only a single type of node and edge. In this work we present muxGNN, a multiplex graph neural network for heterogeneous graphs. To model heterogeneity, we represent graphs as multiplex networks consisting of a set of relation layer graphs and a coupling graph that links node instantiations across multiple relations. We parameterize relation-specific representations of nodes and design a novel coupling attention mechanism that models the importance of multi-relational contexts for different types of nodes and edges in heterogeneous graphs. We further develop two complementary coupling structures: node invariant coupling suitable for node- and graph-level tasks, and node equivariant coupling suitable for link-level tasks. Extensive experiments conducted on six real-world datasets for link prediction in both transductive and inductive contexts and graph classification demonstrate the superior performance of muxGNN over state-of-the-art heterogeneous GNNs. In addition, we show that muxGNN's coupling attention discovers interpretable connections between different relations in heterogeneous networks.

GraphOS: Towards Oblivious Graph Processing

We propose GraphOS, a system that allows a client that owns a graph database to outsource it to an untrusted server for storage and querying. It relies on doubly-oblivious primitives and trusted hardware to achieve a very strong privacy and efficiency notion which we call oblivious graph processing : the server learns nothing besides the number of graph vertexes and edges, and for each query its type and response size. At a technical level, GraphOS stores the graph on a doubly-oblivious data structure , so that all vertex/edge accesses are indistinguishable. For this purpose, we propose Omix++, a novel doubly-oblivious map that outperforms the previous state of the art by up to 34×, and may be of independent interest. Moreover, to avoid any leakage from CPU instruction-fetching during query evaluation, we propose algorithms for four fundamental graph queries (BFS/DFS traversal, minimum spanning tree, and single-source shortest paths) that have a fixed execution trace , i.e., the sequence of executed operations is independent of the input. By combining these techniques, we eliminate all information that a hardware adversary observing the memory access pattern within the protected enclave can infer. We benchmarked GraphOS against the best existing solution, based on oblivious relational DBMS (translating graph queries to relational operators). GraphOS is not only significantly more performant (by up to two orders of magnitude for our tested graphs) but it eliminates leakage related to the graph topology that is practically inherent when a relational DBMS is used unless all operations are "padded" to the worst case.

Model Inversion Attacks Against Graph Neural Networks

Many data mining tasks rely on graphs to model relational structures among individuals (nodes). Since relational data are often sensitive, there is an urgent need to evaluate the privacy risks in graph data. One famous privacy attack against data analysis models is the model inversion attack, which aims to infer sensitive data in the training dataset and leads to great privacy concerns. Despite its success in grid-like domains, directly applying model inversion attacks on non-grid domains such as graph leads to poor attack performance. This is mainly due to the failure to consider the unique properties of graphs. To bridge this gap, we conduct a systematic study on model inversion attacks against Graph Neural Networks (GNNs), one of the state-of-the-art graph analysis tools in this paper. Firstly, in the white-box setting where the attacker has full access to the target GNN model, we present GraphMI to infer the private training graph data. Specifically in GraphMI, a projected gradient module is proposed to tackle the discreteness of graph edges and preserve the sparsity and smoothness of graph features; a graph auto-encoder module is used to efficiently exploit graph topology, node attributes, and target model parameters for edge inference; a random sampling module can finally sample discrete edges. Furthermore, in the hard-label black-box setting where the attacker can only query the GNN API and receive the classification results, we propose two methods based on gradient estimation and reinforcement learning (RL-GraphMI). With the proposed methods, we study the connection between model inversion risk and edge influence and show that edges with greater influence are more likely to be recovered. Extensive experiments over several public datasets demonstrate the effectiveness of our methods. We also evaluate our attacks under two defenses: one is the well-designed differential private training, and the other is graph preprocessing. Our experimental results show that such defenses are not sufficiently effective and call for more advanced defenses against privacy attacks.

Masked Graph Neural Networks for Unsupervised Anomaly Detection in Multivariate Time Series.

Anomaly detection has been widely used in grid operation and maintenance, machine fault detection, and so on. In these applications, the multivariate time-series data from multiple sensors with latent relationships are always high-dimensional, which makes multivariate time-series anomaly detection particularly challenging. In existing unsupervised anomaly detection methods for multivariate time series, it is difficult to capture the complex associations among multiple sensors. Graph neural networks (GNNs) can model complex relations in the form of a graph, but the observed time-series data from multiple sensors lack explicit graph structures. GNNs cannot automatically learn the complex correlations in the multivariate time-series data or make good use of the latent relationships among time-series data. In this paper, we propose a new method-masked graph neural networks for unsupervised anomaly detection (MGUAD). MGUAD can learn the structure of the unobserved causality among sensors to detect anomalies. To robustly learn the temporal context from adjacent time points of time-series data from the same sensor, MGUAD randomly masks some points of the time-series data from the sensor and reconstructs the masked time points. Similarly, to robustly learn the graph-level context from adjacent nodes or edges in the relation graph of multivariate time series, MGUAD masks some nodes or edges in the graph under the framework of a GNN. Comprehensive experiments are conducted on three public datasets. According to the experimental findings, MGUAD outperforms state-of-the-art anomaly detection methods.

Convolutional-Neural-Network-Based Hexagonal Quantum Error Correction Decoder

Topological quantum error-correcting codes are an important tool for realizing fault-tolerant quantum computers. Heavy hexagonal coding is a new class of quantum error-correcting coding that assigns physical and auxiliary qubits to the vertices and edges of a low-degree graph. The layout of heavy hexagonal codes is particularly suitable for superconducting qubit architectures to reduce frequency conflicts and crosstalk. Although various topological code decoders have been proposed, constructing the optimal decoder remains challenging. Machine learning is an effective decoding scheme for topological codes, and in this paper, we propose a machine learning heavy hexagonal decoder based on a convolutional neural network (CNN) to obtain the decoding threshold. We test our method on heavy hexagonal codes with code distance of three, five, and seven, and increase it to five, seven, and nine by optimizing the RestNet network architecture. Our results show that the decoder thresholding accuracies are about 0.57% and 0.65%, respectively, which are about 25% higher than the conventional decoding scheme under the depolarizing noise model. The proposed decoding architecture is also applicable to other topological code families.

The k-Ramsey number of two five cycles

Given any two graphs F and H, the Ramsey number R(F, H) is defined as the smallest positive integer n such that every red-blue coloring of the edges of the complete graph Kn of order n, there will be a subgraph of Kn isomorphic to F whose edges are all colored red (a red F) or a subgraph of Kn isomorphic to H whose edges are all colored blue (a blue H). If F and H are bipartite graphs, then the k-Ramsey number R k ( F , H ) is defined as the smallest positive integer n such that for any red-blue coloring of the edges of the complete k-partite graph of order n in which each partite set is of order ⌊ n k ⌋ or ⌈ n k ⌉ there will be a subgraph isomorphic to F whose edges are all colored red (a red F) or a subgraph isomorphic to H whose edges are all colored blue (a blue H). Andrews, Chartrand, Lumduanhom and Zhang found the k-Ramsey number R k ( F , H ) for F = H = C 4 , and for F = K 1 , t and H = K 1 , s where s , t ≥ 2 . We continue their work by investigating the case where the graphs F and H are both C 5.