Related papers: Witness (Delaunay) Graphs
In recent years, Dynamic Graph (DG) representations have been increasingly used for modeling dynamic systems due to their ability to integrate both topological and temporal information in a compact representation. Dynamic graphs allow to…
We extend the graph convolutional network method for deep learning on graph data to higher order in terms of neighboring nodes. In order to construct representations for a node in a graph, in addition to the features of the node and its…
In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…
Recently, many systems for graph analysis have been developed to address the growing needs of both industry and academia to study complex graphs. Insight into the practical uses of graph analysis will allow future developments of such…
In this paper, we consider the problem of representing graphs by triangles whose sides touch. As a simple necessary condition, we show that pairs of vertices must have a small common neighborhood. On the positive side, we present linear…
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Graph drawings are commonly used to visualize relational data. User understanding and performance are linked to the quality of such drawings, which is measured by quality metrics. The tacit knowledge in the graph drawing community about…
Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in…
Learning the right graph representation from noisy, multisource data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give…
The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…
Nowadays, the analysis of complex phenomena modeled by graphs plays a crucial role in many real-world application domains where decisions can have a strong societal impact. However, numerous studies and papers have recently revealed that…
The adjacency matrix is the most fundamental and intuitive object in graph analysis that is useful not only mathematically but also for visualizing the structures of graphs. Because the appearance of an adjacency matrix is critically…
Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for…
Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and…
Node representation learning has demonstrated its efficacy for various applications on graphs, which leads to increasing attention towards the area. However, fairness is a largely under-explored territory within the field, which may lead to…