Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.
About 10,000 papers for “Simple graph”
Alexander H. Hartmann, Heiko Rieger · 2001
This chapter contains sections titled: The Connectivity-percolation Problem Hoshen-Kopelman Algorithm Other Algorithms for Connectivity Percolation General Search Algorithms Shortest-path Algorithms The Directed Polymer in a Random Medium Dijkstra's Algorithm Label-correcting Algorithm Minimum Spanning Tree
Cited by 0
James O.Aldrich, Hilda M.Rodr amp guez · 2013
Cited by 0
James O.Aldrich, Hilda M.Rodr amp guez · 2013
Cited by 0
Richard J. Fateman, John L. Chen · 2007
Applications of mathematics occasionally produce models that are best understood and visualized as directed or undirected graphs. Computer aids to mathematicians can contribute to the understanding and communication of this information, especially if well-integrated into the problem-solving working environment of the investigator. This particular exercise was prompted by a paper [1] by a colleague, F. Alberto Grünbaum. The particular need in Grünbaum's paper is to describe a graph relating input and output states via a matrix of probabilities. The paper's illustrative graph is of relatively small size (24 nodes, 60 edges), but its display required careful "manual" rearrangement.
Cited by 0
Zhenbang Xiao, Yu Wang, Shunyu Liu et al. · Lecture notes in computer science · 2024
Cited by 12
Yue Liu, Xihong Yang, Sihang Zhou et al. · arXiv (Cornell University) · 2022
Contrastive learning has recently attracted plenty of attention in deep graph clustering for its promising performance. However, complicated data augmentations and time-consuming graph convolutional operation undermine the efficiency of these methods. To solve this problem, we propose a Simple Contrastive Graph Clustering (SCGC) algorithm to improve the existing methods from the perspectives of network architecture, data augmentation, and objective function. As to the architecture, our network includes two main parts, i.e., pre-processing and network backbone. A simple low-pass denoising operation conducts neighbor information aggregation as an independent pre-processing, and only two multilayer perceptrons (MLPs) are included as the backbone. For data augmentation, instead of introducing complex operations over graphs, we construct two augmented views of the same vertex by designing parameter un-shared siamese encoders and corrupting the node embeddings directly. Finally, as to the objective function, to further improve the clustering performance, a novel cross-view structural consistency objective function is designed to enhance the discriminative capability of the learned network. Extensive experimental results on seven benchmark datasets validate our proposed algorithm's effectiveness and superiority. Significantly, our algorithm outperforms the recent contrastive deep clustering competitors with at least seven times speedup on average.
Cited by 3Open access
J. P. Parry · American Journal of Physics · 1972
First Page
Cited by 0
Yue Liu, Xihong Yang, Sihang Zhou et al. · IEEE Transactions on Neural Networks and Learning Systems · 2023
Contrastive learning has recently attracted plenty of attention in deep graph clustering due to its promising performance. However, complicated data augmentations and time-consuming graph convolutional operations undermine the efficiency of these methods. To solve this problem, we propose a simple contrastive graph clustering (SCGC) algorithm to improve the existing methods from the perspectives of network architecture, data augmentation, and objective function. As to the architecture, our network includes two main parts, that is, preprocessing and network backbone. A simple low-pass denoising operation conducts neighbor information aggregation as an independent preprocessing, and only two multilayer perceptrons (MLPs) are included as the backbone. For data augmentation, instead of introducing complex operations over graphs, we construct two augmented views of the same vertex by designing parameter unshared Siamese encoders and perturbing the node embeddings directly. Finally, as to the objective function, to further improve the clustering performance, a novel cross-view structural consistency objective function is designed to enhance the discriminative capability of the learned network. Extensive experimental results on seven benchmark datasets validate our proposed algorithm's effectiveness and superiority. Significantly, our algorithm outperforms the recent contrastive deep clustering competitors with at least seven times speedup on average. The code of SCGC is released at SCGC. Besides, we share a collection of deep graph clustering, including papers, codes, and datasets at ADGC.
Cited by 159
Farida Abdelmoneum, J. Y. Shi, José M. F. Moura · 2023
Graph classification is typically done with geometric deep learning. Given a set of graphs from different classes, e.g., representing mutagenic and non-mutagenic molecules in the MUTAG dataset, and data defined on the graphs, geometric deep learning architectures such as graph convolutional neural networks and graph attention networks can be used to classify graphs into a set of classes. In this paper, we propose a statistical approach to classify graphs. Unlike deep learning architectures, we design graph features that reflect the graph structure and then build a classifier based on the features. The paper provides an ablation study of our algorithm on various traditional machine learning algorithms and graph classification datasets.
Cited by 1
Luca Pasa, Nicolò Navarin, Wolfgang Erb et al. · IEEE Transactions on Neural Networks and Learning Systems · 2023
Many neural networks for graphs are based on the graph convolution (GC) operator, proposed more than a decade ago. Since then, many alternative definitions have been proposed, which tend to add complexity (and nonlinearity) to the model. Recently, however, a simplified GC operator, dubbed simple graph convolution (SGC), which aims to remove nonlinearities was proposed. Motivated by the good results reached by this simpler model, in this article we propose, analyze, and compare simple graph convolution operators of increasing complexity that rely on linear transformations or controlled nonlinearities, and that can be implemented in single-layer graph convolutional networks (GCNs). Their computational expressiveness is characterized as well. We show that the predictive performance of the proposed GC operators is competitive with the ones of other widely adopted models on the considered node classification benchmark datasets.
Cited by 19Open access
Peer‐Timo Bremer · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2007
The system implements a flexible and extensible scene graph for the visualization and analysis of scientific information.
Cited by 0Open access
Qiang Yu, Xinran Cheng, Shiqiang Xu et al. · arXiv (Cornell University) · 2026
The effectiveness of contrastive learning methods has been widely recognized in the field of graph learning, especially in contexts where graph data often lack labels or are difficult to label. However, the application of these methods to node classification tasks still faces a number of challenges. First, existing data enhancement techniques may lead to significant differences from the original view when generating new views, which may weaken the relevance of the view and affect the efficiency of model training. Second, the vast majority of existing graph comparison learning algorithms rely on the use of a large number of negative samples. To address the above challenges, this study proposes a novel node classification contrast learning method called Simple Network Graph Comparative Learning (SNGCL). Specifically, SNGCL employs a superimposed multilayer Laplace smoothing filter as a step in processing the data to obtain global and local feature smoothing matrices, respectively, which are thus passed into the target and online networks of the siamese network, and finally employs an improved triple recombination loss function to bring the intra-class distance closer and the inter-class distance farther. We have compared SNGCL with state-of-the-art models in node classification tasks, and the experimental results show that SNGCL is strongly competitive in most tasks.
Cited by 0Open access
M. Lino da Silva · 2021
simplegraph project on 'GitHub'.
Cited by 0Open access
Gilbert G. Walter, Martha Contreras · Modeling and simulation in science, engineering & technology · 1999
In this chapter, we concentrate on some of the theoretical concepts and results in graph theory. These are usually intuitive and easy to understand, particularly in terms of the associated diagram. However, there are a lot of definitions to keep straight; furthermore there is no unanimity in the literature about these definitions, so other references may not be helpful. We present the proofs of theorems in some cases as well. These are more difficult than the other materials and can be omitted on first reading.
Cited by 0
Qiang Yu, Xinran Cheng, Shiqiang Xu et al. · ArXiv.org · 2026
The effectiveness of contrastive learning methods has been widely recognized in the field of graph learning, especially in contexts where graph data often lack labels or are difficult to label. However, the application of these methods to node classification tasks still faces a number of challenges. First, existing data enhancement techniques may lead to significant differences from the original view when generating new views, which may weaken the relevance of the view and affect the efficiency of model training. Second, the vast majority of existing graph comparison learning algorithms rely on the use of a large number of negative samples. To address the above challenges, this study proposes a novel node classification contrast learning method called Simple Network Graph Comparative Learning (SNGCL). Specifically, SNGCL employs a superimposed multilayer Laplace smoothing filter as a step in processing the data to obtain global and local feature smoothing matrices, respectively, which are thus passed into the target and online networks of the siamese network, and finally employs an improved triple recombination loss function to bring the intra-class distance closer and the inter-class distance farther. We have compared SNGCL with state-of-the-art models in node classification tasks, and the experimental results show that SNGCL is strongly competitive in most tasks.
Cited by 0Open access
Hoogerwoord, R.R. · Data Archiving and Networked Services (DANS) · 1998
Cited by 0
HUANG Miaomiao, WANG Huiying, WANG Meixia, WANG Yejiang , ZHAO Yuhai · SHILAP Revista de lepidopterología · 2026
Graph data,as a data type with strong expressive power,is difficult to model efficiently due to its complex structure.How to effectively capture its intrinsic information has become a challenging problem.Graph embedding methods have received increasing attention by mapping high-dimensional sparse graphs into low-dimensional dense feature vectors,while preserving the structural information of graphs.However,the existing reviews do not summarize the graph embedding methods comprehensively enough,especially paying less attention to complex graph embedding,which leads to the failure to systematically sort out the current status of research on graph embedding in dealing with diverse graph data.Therefore,this paper presents a systematic review of graph embedding learning methods from simple to complex graphs.Firstly,it gives the common definitions of various types of graphs and graph embedding.Secondly,it systematically summarizes the embedding methods on simple graphs,including shallow and deep embedding methods.Then,it summarizes the embedding methods on complex graphs according to the types of graphs,focusing on the application of deep embedding techniques in complex graph structures such as dynamic graphs,heterogeneous graphs,multiplex graphs,and hypergraphs,to fill the gaps in the existing literature that is insufficiently researched on complex graph structures.Finally,it discusses the practical application scenarios of graph embedding techniques,and looks forward to the future development directions.
Cited by 0Open access
Rashid-Jalal Qureshi, Jean-Yves Ramel, Hubert Cardot · HAL (Le Centre pour la Communication Scientifique Directe) · 2007
International audience
Cited by 0
Ming Chen, Zhewei Wei, Zengfeng Huang et al. · arXiv (Cornell University) · 2020
Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theoretical and empirical evidence that the two techniques effectively relieves the problem of over-smoothing. Our experiments show that the deep GCNII model outperforms the state-of-the-art methods on various semi- and full-supervised tasks. Code is available at https://github.com/chennnM/GCNII .
Cited by 399Open access
Mathieu, Claire, Zhou, Hang · arXiv (Cornell University) · 2021
How efficiently can we find an unknown graph using distance queries between its vertices? We assume that the unknown graph is connected, unweighted, and has bounded degree. The goal is to find every edge in the graph. This problem admits a reconstruction algorithm based on multi-phase Voronoi-cell decomposition and using Õ(n^{3/2}) distance queries [Kannan et al., 2018]. In our work, we analyze a simple reconstruction algorithm. We show that, on random Δ-regular graphs, our algorithm uses Õ(n) distance queries. As by-products, we can reconstruct those graphs using O(log² n) queries to an all-distances oracle or Õ(n) queries to a betweenness oracle, and we bound the metric dimension of those graphs by log² n. Our reconstruction algorithm has a very simple structure, and is highly parallelizable. On general graphs of bounded degree, our reconstruction algorithm has subquadratic query complexity.
Cited by 10Open access