Related papers: Graph connection Laplacian and random matrices wit…

In recent years, graph neural networks (GNN) have achieved significant developments in a variety of graph analytical tasks. Nevertheless, GNN's superior performance will suffer from serious damage when the collected node features or…

Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of…

Recently, much of the existing work in manifold learning has been done under the assumption that the data is sampled from a manifold without boundaries and singularities or that the functions of interest are evaluated away from such points.…

In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via…

In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to…

Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node…

Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs…

Link partitioning is a popular approach in network science used for discovering overlapping communities by identifying clusters of strongly connected links. Current link partitioning methods are specifically designed for networks modelled…

Semi-supervised learning on graph structured data has received significant attention with the recent introduction of Graph Convolution Networks (GCN). While traditional methods have focused on optimizing a loss augmented with Laplacian…

Graph neural networks have developed by leaps and bounds in recent years due to the restriction of traditional convolutional filters on non-Euclidean structured data. Spectral graph theory mainly studies fundamental graph properties using…

We propose a novel mathematical framework to address the problem of automatically solving large jigsaw puzzles. This problem assumes a large image, which is cut into equal square pieces that are arbitrarily rotated and shuffled, and asks to…

Anomaly detection in networks often boils down to identifying an underlying graph structure on which the abnormal occurrence rests on. Financial fraud schemes are one such example, where more or less intricate schemes are employed in order…

Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…

We consider Gallai's graph Modular Decomposition theory for network analytics. On the one hand, by arguing that this is a choice tool for understanding structural and functional similarities among nodes in a network. On the other, by…

Graph Contrastive Learning (GCL) has emerged as a promising approach in the realm of graph self-supervised learning. Prevailing GCL methods mainly derive from the principles of contrastive learning in the field of computer vision: modeling…

Graph Convolutional Networks (GCNs) have been shown to be a powerful concept that has been successfully applied to a large variety of tasks across many domains over the past years. In this work we study the theory that paved the way to the…

In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of…

Graph contrastive learning (GCL) aims to learn discriminative semantic invariance by contrasting different views of the same graph that share critical topological patterns. However, existing GCL approaches with structural augmentations…

Graph contrastive learning (GCL), as a popular approach to graph self-supervised learning, has recently achieved a non-negligible effect. To achieve superior performance, the majority of existing GCL methods elaborate on graph data…

Recently normalized Laplacian matrices of graphs are studied as density matrices in quantum mechanics. Separability and entanglement of density matrices are important properties as they determine the nonclassical behavior in quantum…