Related papers: Comparing Embedded Graphs Using Average Branching …
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…
The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance however…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…
Graph embedding is a transformation of vertices of a graph into set of vectors. Good embeddings should capture the graph topology, vertex-to-vertex relationship, and other relevant information about graphs, subgraphs, and vertices. If these…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
The Frechet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to handwriting recognition. More recently, the Frechet distance has been generalized to a…
Any planar graph has a crossing-free straight-line drawing in the plane. A simultaneous geometric embedding of two n-vertex graphs is a straight-line drawing of both graphs on a common set of n points, such that the edges withing each…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Physical phenomena in science and engineering are frequently modeled using scalar fields. In scalar field topology, graph-based topological descriptors such as merge trees, contour trees, and Reeb graphs are commonly used to characterize…
Graph embedding is the task of representing nodes of a graph in a low-dimensional space and its applications for graph tasks have gained significant traction in academia and industry. The primary difference among the many recently proposed…
Graph embeddings deal with injective maps from a given simple, undirected graph $G=(V,E)$ into a metric space, such as $\mathbb{R}^n$ with the Euclidean metric. This concept is widely studied in computer science, see \cite{ge1}, but also…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
Merge trees, contour trees, and Reeb graphs are graph-based topological descriptors that capture topological changes of (sub)level sets of scalar fields. Comparing scalar fields using their topological descriptors has many applications in…
Metric graphs are meaningful objects for modeling complex structures that arise in many real-world applications, such as road networks, river systems, earthquake faults, blood vessels, and filamentary structures in galaxies. To study metric…