Related papers: Towards a classification of planar maps
Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…
Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e. the question of how good an algorithm…
Streets are large, diverse, and used for several (and possibly conflicting) transport modalities as well as social and cultural activities. Proper planning is essential and requires data. Manually fabricating data that represent streets…
Network (or Graph) Alignment Algorithms aims to reveal structural similarities among graphs. In particular Local Network Alignment Algorithms (LNAs) finds local regions of similarity among two or more networks. Such algorithms are in…
We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property pi is called a pi-graph. If pi satisfies certain properties, then an n-node m-edge pi-graph G can…
Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world…
Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph…
Structure inference is an important task for network data processing and analysis in data science. In recent years, quite a few approaches have been developed to learn the graph structure underlying a set of observations captured in a data…
Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they…
We prove that for any parameter r an r-locally 2-connected graph G embeds r-locally planarly in a surface if and only if a certain matroid associated to the graph G is co-graphic. This extends Whitney's abstract planar duality theorem from…
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general…
Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level…
The significant increase in world population and urbanisation has brought several important challenges, in particular regarding the sustainability, maintenance and planning of urban mobility. At the same time, the exponential increase of…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
We study the \emph{picture space} $X^d(G)$ of all embeddings of a finite graph $G$ as point-and-line arrangements in an arbitrary-dimensional projective space, continuing previous work on the planar case. The picture space admits a natural…
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…
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in $\mathbb{R}^n$, we may obtain a global representation as a cell complex with vertices given by a representative subset of the point cloud. The vertex…
A map $\varphi:K\to R^2$ of a graph $K$ is approximable by embeddings, if for each $\varepsilon>0$ there is an $\varepsilon$-close to $\varphi$ embedding $f:K\to R^2$. Analogous notions were studied in computer science under the names of…
Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…