相关论文: Witness (Delaunay) Graphs

We argue that when comparing two graphs, the distribution of node structural features is more informative than global graph statistics which are often used in practice, especially to evaluate graph generative models. Thus, we present…

Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically,…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

Graphs have become pervasive tools to represent information and datasets with irregular support. However, in many cases, the underlying graph is either unavailable or naively obtained, calling for more advanced methods to its estimation.…

We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that…

Urban regions are complicated functional systems that are closely associated with and reshaped by human activities. The propagation of online geographic information-sharing platforms and mobile devices equipped with Global Positioning…

This paper introduces a visibility relation $v$ (and the strong visibility relation $\mathop{v}\limits^{\doublewedge}$) on proximal Delaunay meshes. A main result in this paper is that the visibility relation $v$ is equivalent to Wallman…

Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…

Graph neural networks (GNN) have shown outstanding applications in many fields where data is fundamentally represented as graphs (e.g., chemistry, biology, recommendation systems). In this vein, communication networks comprise many…

In a labeling scheme the vertices of a given graph from a particular class are assigned short labels such that adjacency can be algorithmically determined from these labels. A representation of a graph from that class is given by the set of…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…

Graphs are widely used to describe real-world objects and their interactions. Graph Neural Networks (GNNs) as a de facto model for analyzing graphstructured data, are highly sensitive to the quality of the given graph structures. Therefore,…

Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…

Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…

In a witness rectangle graph (WRG) on vertex point set P with respect to witness points set W in the plane, two points x, y in P are adjacent whenever the open isothetic rectangle with x and y as opposite corners contains at least one point…

Graph deep learning methods have become popular tools to process collections of correlated time series. Unlike traditional multivariate forecasting methods, graph-based predictors leverage pairwise relationships by conditioning forecasts on…

Graph Neural Networks (GNNs), neural network architectures targeted to learning representations of graphs, have become a popular learning model for prediction tasks on nodes, graphs and configurations of points, with wide success in…

As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for…

Studying the behavior of crowds is vital for understanding and predicting human interactions in public areas. Research has shown that, under certain conditions, large groups of people can form collective behavior patterns: local…

Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a…