Top Research Papers on Graph Theory

This book provides an extensive set of tools for applying fuzzy mathematics and graph theory to real-life problems. Balancing the basics and latest developments in fuzzy graph theory, this book starts with existing fundamental theories such as connectivity, isomorphism, products of fuzzy graphs, and different types of paths and arcs in fuzzy graphs to focus on advanced concepts such as planarity in fuzzy graphs, fuzzy competition graphs, fuzzy threshold graphs, fuzzy tolerance graphs, fuzzy trees, coloring in fuzzy graphs, bipolar fuzzy graphs, intuitionistic fuzzy graphs, m-polar fuzzy graphs...

The study of sampling signals on graphs with the goal of building an analog of sampling for standard signals in the time and spatial domains is reviewed, focusing on theory and potential applications.

Spectral clustering converts the data clustering problem to the graph cut problem. It is based on graph theory. Due to the reliable theoretical basis and good clustering performance, spectral clustering has been successfully applied in many fields. Although spectral clustering has many advantages, it faces the challenges of high time and space complexity when dealing with large scale complex data. Firstly, this paper introduces the basic concept of graph theory, reviews the properties of Laplacian matrix and the traditional graph cuts method. Then, it focuses on four aspects of the realization...

This article discusses the basic graph theory concepts and the various graph types, as well as the available data structures for storing and reading graphs, and describes several network properties.

This update describes new features and enhancements introduced over many new versions from 2015 to 2022 of Cytoscape.js, an open-source JavaScript-based graph library used to render interactive graphs in a web browser.

It is proved that GNNs achieve near-optimal performance in wireless networks with much fewer training samples than traditional neural architectures and proposed design guidelines are proposed, which includes graph modeling, neural architecture design, and theory-guided performance enhancement.

The current review illustrated changed global network organization of structural and functional brain connectomes in MDD compared to HC and were varied according to the onset age and medication status.

The mean phase coherence method, based on the “phase-locking value,” was the most frequently used functional estimation technique in the reviewed studies and the unweighted functional brain network has received substantially more attention in the literature than the weighted network.

OBJECTIVE: Analysis of functional and structural brain networks has suggested that major depressive disorder (MDD) is associated with a disruption in brain networks. This paper aims to investigate the abnormalities of brain networks in MDD. APPROACH: To this aim, we constructed weighted directed functional networks based on electroencephalography (EEG) signals of 26 MDD patients and 23 normal (N) subjects. The nodes of networks were 19 EEG electrodes, and the edges were phase transfer entropy (PTE) between each pair of electrodes. PTE is a model-free, phase-based effective connectivity measure...

A new model, known as Graph Transformer, is proposed that uses explicit relation encoding and allows direct communication between two distant nodes and provides a more efficient way for global graph structure modeling.

The role of graph convolutional filters in GNNs is discussed and it is shown that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topology.

Experimental results show that AGE consistently outperforms state-of-the-art graph embedding methods considerably on node clustering and link prediction tasks, and the proposed Adaptive Graph Encoder employs an adaptive encoder that iteratively strengthens the filtered features for better node embeddings.

This work proposes ROLAND, an effective graph representation learning framework for real-world dynamic graphs that can help researchers easily repurpose any static GNN to dynamic graphs and proposes a scalable and efficient training approach for dynamic GNNs via incremental training and meta-learning.

This article proposes a graph-in-graph (GiG) model and a related GiG convolutional network (GiGCN) for HSI classification from a superpixel viewpoint and is the first to propose the GiG framework from the superpixel point and the GiGCN scheme for H SI classification.

This paper systematically reviews graph-based analysis methods of Graph Signal Processing, Graph Neural Networks and graph topology inference, and their applications to biological data, and covers the Graph Fourier Transform and the graph filter developed in GSP.

A new way to implement multiscale extraction via constructing Haar-type graph framelets with desired properties of permutation equivariance, efficiency, and sparsity, for deep learning tasks on graphs is developed.

This study is aimed at providing a broad, complete as well as comprehensive overview of GNN-based technologies for solving four different KG tasks, including link prediction, knowledge graph alignment, knowledge graphs reasoning, and node classification.

Differentiable Graph Module is introduced, a learnable function predicting the edge probability in the graph relevant for the task, that can be combined with convolutional graph neural network layers and trained in an end-to-end fashion and achieves state-of-the-art results.

This work makes the first attempt towards learning an optimal heterogeneous graph structure for HGNNs and proposes a novel framework HGSL, which jointly performs Heterogeneous Graph Structure Learning and GNN parameters learning for classification task.

Graph representation learning resurges as a trending research subject owing to the widespread use of deep learning for Euclidean data, which inspire various creative designs of neural networks in the non-Euclidean domain, particularly graphs. With the success of these graph neural networks (GNN) in the static setting, we approach further practical scenarios where the graph dynamically evolves. Existing approaches typically resort to node embeddings and use a recurrent neural network (RNN, broadly speaking) to regulate the embeddings and learn the temporal dynamics. These methods require the kn...